No more and not any more are determiners and adverbs.
No more, not any more as determiners
We use no more and not any more as determiners to talk about an absence of something that was once there. No more is more formal than not any more:
I will ask no more questions. (formal)
I won’t ask any more questions. (informal)
There’s no more cake. They’ve eaten it all. (or There isn’t any more cake.)
No more, not any more as adverbs
We use no more and not any more as adverbs to talk about something stopping or ending. No more is more formal than not any more:
The army has arrived. We should fear no more. (formal)
I wouldn’t worry any more if I was you. Everything will be okay. (informal)
No more … than, Not any more … than
We use no more … than or not any more … than to talk about comparative quantities and degrees. No more than is more formal than not any more than:
It does not tell you much. There is no more detail than in the instructions. (formal)
Flying there isn’t any more expensive than getting the train. (informal)
Writing: any more or anymore?
In British English we usually write the adverb any more as two words though we sometimes see it as one word, especially in American English. We never write it as one word as a determiner:
I’m not cold any more. (or I’m not cold anymore.)
I can’t print any more copies. The printer isn’t working.
I can’t print anymore copies.