Entailment differs from implication, where the truth of one suggests the truth of the other, but does not require it. For example, the sentence Mary had a baby and got married implicates that she had a baby before the wedding, but this is cancellable by adding -- not necessarily in that order. Entailments are not cancellable.
Entailment also differs from presupposition in that in presupposition, the truth of what one is presupposing is taken for granted.