From what I understand, they both mean "is not". But from what I've been able to gather from the few times I've heard it, it seems that あるまい may not be as strong or definitive as ありません. Am I on the right track here? Also, can まい be used with any verb ex: 飲むまい or just with ある?
ませんexpresses negation in polite form.
まいexpresses a guess or intentional future, both in negation. So its entailment is weaker than
ません, but implies willingness. A close counterpart in English is
shall notas opposed to
まいcan be used with other verbs as well.
'I will not drink liquor any more.' (polite)
'I shall not drink liquor any more.' (guess)
'I shall not drink liquor any more.' (declaration)