This is a matter of "slots" indeed, although not in any particularly defined sense.
See, Dungeon Master's Guide, page 141 (or here) mentions the following:
"Use common sense to determine whether more than one of a given kind of magic item can be worn. A character can't normally wear more than one pair of footwear, one pair of gloves or gauntlets, one pair of bracers, one suit of armor, one item of head wear, and one cloak. You can make exceptions; a character might be able to wear a circlet under a helmet, for example, or be able to layer two cloaks."
Note that the cloak is on the fringe of the exception. A DM may allow you to wear two cloaks, but he may not.
"An item can be attuned to only one creature at at a time, and a creature can be attuned to no more than three magic items at a time."
"Additionally, a creature can't attune to more than one copy of an item."
As mentioned, your DM may allow you to wear any combination of items that seems reasonable. A light weight cloak made of silk might well be wearable with a second cloak if the DM thinks it reasonable. A headband might be wearable with a magical helmet. Fifth edition has replaced the slot limitations of the previous editions with the attunement system. Many magic items including those mentioned must be attuned before the character receives any benefit. A character has a limit of three attuned items at a time. In addition, the character can not attune any items with the same name (for example if you ran across a "ring of protection +1" and a "ring of protection +2" you could not use both since they are both called a "ring of protection").
Of course you are free to change attuned items ... it just takes a short rest for each. However, they are still limited to a maximum of three different attunable magic items which actually makes balancing things out a lot easier.
I brought up this ruling last session with our Cleric. We have 2 Pearls of Power. I was all, "Use the Pearl. Short rest and drop the attunement. Next short rest, attune to the other Pearl of power and use it before both recharge at dawn.".
"Some magic items require a creature to form a bond with them before their magical properties can be used. This bond is called attunement, and certain items have a prerequisite for it. If the prerequisite is a class, a creature must be a member of that class to attune to the item. (If the class is a spellcasting class, a monster qualifies if it has spell slots and uses that class's spell list.) If the prerequisite is to be a spellcaster, a creature qualifies if it can cast at least one spell using its traits or features, not using a magic item or the like. Without becoming attuned to an item that requires attunement, a creature gains only its nonmagical benefits, unless its description states otherwise. For example, a magic shield that requires attunement provides the benefits of a normal shield to a creature not attuned to it, but none of its magical properties. Attuning to an item requires a creature to spend a short rest focused on only that item while being in physical contact with it (this can't be the same short rest used to learn the item's properties). This focus can take the form of weapon practice (for a weapon), meditation (for a wondrous item), or some other appropriate activity. If the short rest is interrupted, the attunement attempt fails. Otherwise, at the end of the short rest, the creature gains an intuitive understanding of how to activate any magical properties of the item, including any necessary command words. An item can be attuned to only one creature at a time, and a creature can be attuned to no more than three magic items at a time. Any attempt to attune to a fourth item fails; the creature must end its attunement to an item first. Additionally, a creature can't attune to more than one copy of an item. For example, a creature can't attune to more than one ring of protection at a time. A creature's attunement to an item ends if the creature no longer satisfies the prerequisites for attunement, if the item has been more than 100 feet away for at least 24 hours, if the creature dies, or if another creature attunes to the item. A creature can also voluntarily end attunement by spending another short rest focused on the item, unless the item is cursed.
The reason dates back to older editions wear rings were commonly enchanted and has a feat specifically for crafting them while cloaks fell into the miscellaneous category and therefore required the higher "Craft Wondrous Item" feat
Look up Combining Game Effects and Combining Magical Effects. If something does the same things as another thing, you only gain the best benefit, not the full benefit of both.
From these small blurbs in the rules, I would infer you cannot benefit from a cloak of protection and a ring of protection nor, from two rings of protection, for example.
The DMG says " Additionally, a creature can’t attune to more than one copy of an item." It doesn't mention effects. As I read this, two rings of protection are a no go, but a ring and a cloak are just fine. This makes sense - a "no duplication of effects" rule would be difficult to implement. For example, would that mean that you couldn't attune to both a luckstone and a ring of protection because both give a +1 to saving throws?
The PHB "combining effects" rules seem to be limited to preventing you from "double blessing" somebody by casting bless on them twice and things of that nature - not the benefits of magic items.
I also note that DnD Beyond does not implement this rule at all. It lets you attune three rings of protection if you want.
This is posted in Rules and Game Mechanics, therefore, I am referring to the game rules that adress this question. If you personally house rule otherwise, or don't get the same understanding that I do from these rules, that is fine.
Someone pointed this out to me before, the builder won't stop you from equiping items. I just put two breastplates on for fun.
If you read carefully, this passage refers to "Game Features" that include spells, class features, feats, racial traits, monster abilities and magic items.
My interpretation, if the naming convention is the same as are the bonuses, they do not stack. As in "of protection" regardless of what the items are physically.
Naming convention does not matter. It is explicitly applicable to things that have the same full name. Instances where the name is different, but the rule does apply--such as Thirsting Blade with Extra Attack--are explicitly stated to not stack in their descriptions.
If you cannot benefit from a ring/cloak at the same time, you cannot benefit from a +1 shield & +1 armor at the same time either, and that's clearly absurd.
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You don't know what fear is until you've witnessed a drunk bird divebombing you while carrying a screaming Kobold throwing fire anywhere and everywhere.
For what it's worth, per the sage advice compendium, "In general, bonuses stack, unless they're from the same spell. You also can't benefit from more than one ring of protection, for instance, since you can't attune to more than one copy of an item at a time."
This was in response to a question about whether a ring of protection and bracers of defense stack (they do). Note it only references a "copy of an item" and says nothing about naming conventions.
Is there a limit of two rings? I don't recall seeing that old rule in 5e
There is no rule on number of rings beyond having enough fingers or other appropriate appendages to wear them.
The ring and cloak do stack (they're different items) and this is why one is uncommon and one is rare: so you're not stacking them at lower levels. You'll get the cloak relatively earlier (uncommon) and only later (rare) can you get the ring to basically double the effect.
So a Cloak of Protection does the exact same thing as a Ring of Protection. Both give +1 to Ac and +1 to Saves. One is rare, the other is uncommon.
The odd thing, far as I know is that you can only have one cloak....but you can have 2 rings.
For AL, the 'more than one ring (not just 2)' is offset by the cloak costing 16 TP (points can be of any tier), but the ring costs 20 TP (points must be tiers 2-4). ...and anyone belonging to the Order of the Gauntlet has the potential to buy it for a measly 500gp and 50 days downtime (some version of that option will hopefully show up in Season 9 as that's as of Season 7, with Season 8 making it almost impossible to get enough Faction rank to unlock that option), which means some characters don't even need to go find it.
Considering all that, in my opinion, the cloak is probably better than the ring...at least in AL. At home, the ring is probably better if I had to pick just one.