I'm trying figure this out and wanted to figure out a good ruling for this. My players are arguing that because items are magical they do magical damage. My arguement is that the magic within certain items are magical because of the specific properties given to them and that it has to be specifically damage that gives the magical damage. My example is that if a monk has winged boots and bracer of defense their unarmed attacks are still not magical or throwing an alchemy jug at an enemy isnt magical bludgeoning. What do you guys think?

Items do not do magical damage unless it is stated they are a magical weapon, even if they are used as an improvised weapon.

Spells do magical/spell damage AND any other damage type listed in the spell description.

So at 6th level a Monk has the ability to count their unarmed strikes (or strikes with a monk weapon) as magical weapons, with no bonuses.  Thus overcoming regular resistance/immunity.  So 5th level Monk can punch a Werewolf all day and not do any damage, a 6th level Monk will do full damage to the same Werewolf.

Mechanically, there's no "magical damage". It's damage from a magical source.
A +1 longsword still does "slashing" damage, it's just that the source is magical, so it overcomes resistence.

For those improvised attacks, it's up to you to put the Master into Dungeon Master.
I can see me going either way on those depending on the campaign.

I forgot to add that they also mentioned the common magic items in XGtE. The moon touched sword and unbreakable arrow doing magical slashing and piercing respectively. I did say because it doesnt explicitly say so it is going to be non magical damage despite the magic item properties. I think if they were at higher levels or a high magic campaign I would rule yes but at level three I ruled no. 

Both of those would be no, look at the differences between them and any +1 weapon or ammunition.  There would be nothing wrong having a Moon Touched Longsword +1 (combining the two for whatever reason), but a Moon Touched Longsword by itself would never be magical unless Magic Weapon was cast upon it or through some Magic Item Creation downtime activities.

Their "theory" boils down to is that if someone was to cast Light (a cantrip on every spell list) on anything, then it would become a magical weapon.  That simply is not the case.

Erm, the Moon Touched Sword is on the magic item list, therefore it is a magical weapon and would ignore resistances / immunities against non magical. 
Your comparison on the other Hand is right as it doesn't make it a magical weapon by casting light on it, but is a flawed comparison as one is a created magical item and the other a simple cantrip.
A moon touched sword even banishes the darkness spell.

I usually rule that the moon touched sword does count as a magic weapon, but I wouldn't rule that punching someone with a magic ring counts. 

Quote from Mythos_ZyZyX >>

I'm trying figure this out and wanted to figure out a good ruling for this. My players are arguing that because items are magical they do magical damage. My arguement is that the magic within certain items are magical because of the specific properties given to them and that it has to be specifically damage that gives the magical damage. My example is that if a monk has winged boots and bracer of defense their unarmed attacks are still not magical or throwing an alchemy jug at an enemy isnt magical bludgeoning. What do you guys think?

Everything described here falls under the 'improvise' action and it's entirely up to the DM how to rule it. 

I'd flip it on it's head though...ask the players if they'd be happy taking magical bludgeoning damage that circumvents their resistances from something as simple as stubbing their toe on an unworn piece of armour. Of course they wouldn't.

5e gives players so many ways to gain advantages, deal extra damage, and do incredible and silly things...it's kinda petulant of the players to be asking for magical damage to apply to a thrown alchemy jug etc.

Make it as simple, as 'that's not how I rule it, end of debate'.

Let's look to the rules here.

Particular creatures are even resistant or immune to damage from non-magical attacks (a magical attack is an attack delivered by a spell, a magic item, or another magical source).

From the Monster Manual. Now, the Moon-Touched Sword group are explicitly magic items. Which means any DM ruling they don't deal magical damage is wrong, period. Now, improvised weapons are a different beast. There's nothing specifically ruling that an item that's not meant to function as a weapon would count as magical damage if a player character attacks with it. But if a DM decides to rule that it counts that way in their games, that's up to them. I personally rule no on that one, as the intent of the item's design is important.

If you're the DM, it's your call. But...I would say that only magic 'weapons' deal magic damage. Magic 'items' do not even if thrown or used as as improvised weapons.

I would include the 'NO' to include casting light or another 'utility' spell on a non-magical weapon. Casting a utility spell on a weapon doesn't infer that the weapon is magical. Just that it has a temporary effect on it.

Oh, yeah, the cantrip trick absolutely doesn't work. There's spells you can cast on weapons that specify they make the weapon magical. No reason that a spell that doesn't would do that.