"I wear a black t-shirt."
Translation:Saya memakai kaus hitam.
"pakai" (verb) is the base word.
"memakai" is the base word + "me-" prefix , making it a transitive verb.
The formal way is to use the "me-" prefix.
There is no difference in meaning between these two.
"pake" is how it's often used (pronounced) in daily conversation, but that's not the official spelling.
It's often spelled and pronounced like that.
In daily speech it doesn't really matter.
The issue is, the official spelling is "kaus", and not "kaos" (that has another definition).
See KBBI links:
kaus = t-shirt
kaos = chaos