"Is mise Iain"
Translation:I am Iain
Is mise uses the copula is and is used to state who I am. Tha mi uses the bi verb and is used to describe me: state what I look or feel like, where I am, from where I am, etc.
bi and the copula is are two entirely different verbs that both translate to English to be, but only the copula is used with noun phrase predicates (ie. to define and equate – or classify and identify – things, state what or who something or someone is); while bi is typically used with adjectives, adverbs, and prepositional phrases as the predicate.
Later in the course you'll get sentences like 'is tusa mo charaid' (you are my friend) or 'chan eil mi sgìth, tha thusa sgìth!' (I am not tired, YOU are tired!) Mise is like thusa, it adds extra emphasis on the subject of the sentence. There are better explanations but that's how I remember it, would make sense if you introduce yourself :)
Edit: I wrote 'tha thusa' instead of 'is tusa' because tha mi sgìth
tha thusa mo charaid – that would not be grammatical. As I wrote in my reply above – you need is here, so is tusa mo charaid (thusa is delenited to tusa after is because it ends in dental s).
You are right that there is a difference between regular pronouns mi, thu, and emphatic ones mise, thusa; but the more important difference here is one between substantive verb bi (in tha thusa sgìth) and the copula is (is tusa mo charaid).