Is Arcane Armor technically magic armor? Because when you look at the ability Arcane Armor it doesn't really say it, only says that it can be used as a spellcasting focus which aren't magic items.

Your metallurgical pursuits have led to you making armor a conduit for your magic. As an action, you can turn a suit of armor you are wearing into Arcane Armor, provided you have smith’s tools in hand.

You gain the following benefits while wearing this armor:

• If the armor normally has a Strength requirement, the arcane armor lacks this requirement for you.
• You can use the arcane armor as a spellcasting focus for your artificer spells.
• The armor attaches to you and can’t be removed against your will. It also expands to cover your entire body, although you can retract or deploy the helmet as a bonus action. The armor replaces any missing limbs, functioning identically to a limb it replaces.
• You can doff or don the armor as an action.

Without any other context, no.

If the armor you were wearing before it transformed was already "magic" or infused, then yes. 

Red herring.

The context would be that in my campaign the players fought a black pudding, the armorer artificer tried telling me that his armor was magical because of Arcane Armor so the acid didn't corrode his armor. The information is vague on the ability information, and wanted to make sure that I was not overthinking the ability.

You are indeed correct. Unless the base armor already had a magical effect, it should corrode since it is still mundane as far as RAW is concerned. It sucks, but nothing you can do unless a homebrew solution can be agreed upon.

Depends on how you define Arcane Armor. It gives magical abilities and remains 'arcane armor' until you die or make a different set of armor your arcane armor. The only other thing to really compare the ability to is infusing an item.

Unless it states it is magical armor, then it is not magical armor. If the armor that was made into Arcane Armor magical or it has infusions, then it is magical.

Think of the steel defender when you think of arcane armor. The steel defender is not magical and yet, how it is described how the artificer makes it is quite "magical", but it is NOT magical. The arcane armor is the same way. How it is made sounds "magical", but is is not magical.

You could also think of it like a spellcasting focus. Arcane, holy, and druidic foci aren't magical unless specifically stated to be, like if it's a magic item you're using as a focus. Consider weapons with ruby of the war mage applied - the ruby doesn't make the weapon magical, it just allows the wielder to use it as a spellcasting focus. The Arcane Armor feature works the same way, by making a set of armor special and usable as a focus, but not magical unless the base armor was magical, or if it's been infused.

Lesson to your Armorer is to Infuse their armor to prevent corrosion!

Quote from sfPanzer >>

There are plenty arguments both ways. Technically the official fluff is that the Artificer's infusions are prototype magical items and since the Arcane Armor is likely infused with something like Enhanced Defense it's pretty much a prototype magic armor. On its own it's not really a magic armor though.

If you really don't want to give the Artificer the full benefit of making a magic armor themselves then you could go for a compromise and say it registers as magic armor for detection spells etc. but it doesn't have the full magical protection of proper magic armors yet. I don't see why that should be necessary though and you gotta think about the future as the Artificer will potentially end up with several of their gear infused instead of using some random magic armor you give them and then it would really suck for them to not have the same benefits as others even though it does the same as any other proper armor +1 (in case of Enhanced Defense)

Correct, and I bet the wording is deliberately vague because of that reason. Especially considering that the arcane armor already mimics multiple common magic items, Prosthetic Limb,  Ruby of the War Mage (or whichever one you want to be a focus), Cast-Off Armor (not sure if there is one to don armor in a round).

I'd be really surprised if your armorer doesn't already have an infusion on their armor. Anything with an Infusion attached is considered a magic item, and I feel like the game assumes anyone who takes the armorer subclass will have infused their armor at some point, but I guess it's not a guarantee.