Full Idea
Implication involves some form of link or causality between the antecedent and the consequent of an if-then; normally it says that the conclusion is a consequence of the premise (where conditionals are just defined by 'true' and 'false').
Gist of Idea
Where a conditional is purely formal, an implication implies a link between premise and conclusion
Source
Keith Devlin (Goodbye Descartes [1997], Ch. 2)
Book Reference
Devlin,Keith: 'Goodbye Descartes: the end of logic' [Wiley 1997], p.48
A Reaction
This distinction is a key one when discussing 'If-then' sentences. Some are merely formal conditionals, but others make real claims about where you can get to from where you are.