Are nobles and peers the same thing?

Sort of. To take the UK as our example, peerage is a subset of the nobility, with privileges such as membership in the House of Lords. Only dukes/duchesses, marquesses/marchionesses, earls and countesses, viscounts and viscountesses, and barons and baronesses are considered peers. However, the nobility also includes baronets, knights and dames if one is using the stricter definition, and esquires, landed gentlemen, and other “argimerous families,” if one is using the looser definition. 

It’s further complicated because the peerage traditionally only passed to the heir of the title, so the younger siblings would be considered noble or aristocratic but not peers.