Learn English – “No more”, “no longer”, “not anymore”

Basically, the positive anymore does not simply have the meaning of nowadays, but rather means simply quite the opposite of negative anymore. The negative anymore implies that what is described by the sentence used to be the case, and asserts that it no longer is, the positive anymore implies or asserts that what is described used to NOT be the case, and asserts that it is now.

Kindle and Sag (1975) provide a slightly more technical explanation. Consider the following:

(1) Anymore, we eat a lot of fish.

According to Kindle and Sag (1975):

The usual hypothesis advanced about the grammars of those, primarily Mid-west, speakers who say sentences like [(1)] is that they have restructured anymore into a free-wheeling lexical item with the meaning of 'nowadays'. [...] This explanation has recently been shown to be unsatisfactory by Labov (1972), who observes that all English speakers balk at items like [(3)] and [(4)].

^{(Kindle and Sag 1975:89)}

(3) When would like to live, 1920 or anymore?

(4) When was the best beer brewed? ... Anymore.

Kindle and Sag continue, quoting Labov (1972):

'In Standard English a sentence of the form: 'I don't do Y anymore' presupposes that 'X used to do Y'. In these 'positive' anymore dialects a complex semantic change has taken place creating a new lexical item anymore-2, which occurs only in positive sentences. Positive sentences of the form: 'X does Y anymore' assert that 'X didn't used to do Y.' Positive anymore speakers still have the old anymore in negative sentences, i.e. as a polarity alternant of still.'

^{(Labov 1972, cited by Kindle and Sag 1975:89-90)}

^References

^{Kindle, D. and I. Sag. (1975). Some more on anymore. In R. W. Fasold and R. W. Shuy (eds.), Analyzing variation in language: Papers from the Second Colloquium on New Ways of Analyzing Variation. Washington, D.C. Georgetown University Press, 89-111.}

^{Labov, W. (1972). Where do grammars stop? In R. Shuy (ed.), *Georgetown University Round Table on Languages and Linguistics 1972. Washington, D.C. Georgetown University Press.}

I would say that there is no longer a distinction between them, where any longer was once more formal.

Any more: the two words are the traditional expression in English and may be preferable for formal writing, particularly in a negative expression when meaning “any longer”. The two adverbs are interchangeable, and you can use them in formal and informal writing.

any more (adverb) any longer I couldn't trust him any more.

The only distinction I would make is when it refers to degree: I don't love him any more than I love her. Clearly any longer is not synonymous in this case.