As apposed to the conjunction ā, me is used as a conjunction for two objects/things as apposed to two sentences. Note the differences in the following sentences:
Inanahi, I haere au ki te toa ki te hoko i te paraoa me te miraka, ā, i haere au ki te kura ki te ako.
I went to the shop to buy the bread and the milk, and I went to school to learn.
me is co-ordinating the two object/things (bread and milk) whereas ā is co-ordinating two sentences.