Person A is talking to Person B. Person A says that Person B’s girlfriend has no personality, is only interested in Person B’s money and has negatively impacted Person B’s manners, wardrobe and personal cleanliness since knowing her.

Person A is implying (suggesting, indicating but not stating directly) that Person B might consider breaking up with his girlfriend.

If Person B hears the implication and gets the same idea, he is correctly inferring (deducing, concluding) what Person A is suggesting.

If you suggest a course of action or change of perspective without directly stating it, you are implying something. If someone picks up what you are implying, then they are inferring what you are saying.

And if Person B hears all these things that Person A is implying regarding his girlfriend and he infers that she’s great and he should continue dating her, then he is inferring incorrectly and is probably kind of stupid.