The classic literature refers to the problem where information asymmetry exists between an informed and an uninformed counterpart as the adverse selection problem, but how can we verify what kind of such a game is? Namely, how can we know that such a game is a screening game or a signaling one?
Signaling is the informed side taking actions to reduce (or maintain, depending on the private types) the information asymmetry. For example, high skill workers getting certifications to signal their productivity so as earn a higher wage. Or low skill workers trying to mimic the high-skilled's behavior as much as possible so that they cannot be separated.
Screening is the uninformed side taking actions to reduce the information asymmetry. For example, monopolists use price discrimination strategies to identify customers with high vs low willingness to pay and charge them accordingly.