What is the difference between inference and entailment ?

Same fact. Different expressions of the fact. A reasoning person infers the conclusion from the premises. The premises entail the conclusion. The two sentences are saying substantially the same thing in different words. read more

Basically, an inference is an informal and less reliable kind of entailment. Of course, good inferences tend to use premises that are probably true even if technically unconfirmed, which makes them very, very close to entailments. read more

An entailment is a necessary implication: an inference from an utterance which must be true if the utterance is true. An implicature is a cancellable implication: an inference from an utterance which we take the utterance to imply on its face, by 'default', but which may in the context of other information nonetheless not be true even if the utterance is true. read more

The difference between entailment and inference is that inference procedures cannot necessarily find everything that can be entailed and inference procedures are not necessarily correct/sound (i.e. can derive things that aren't necessarily true). read more