The technical term for someone who is actually "on the bench" for a football (soccer) match in the UK is "a substitute". A "reserve" may commonly be used to describe the same person, but is more correctly used to describe someone who is 'owned' by the same team, but isn't on the team-sheet that day, so isn't officially allowed to play - part of 'the squad' but not part of the official team.
To use a current example, at the Rugby World Cup, a squad will contain approx 30 players; the starting line-up will be just 15, but there will be another 5 on the bench - these are the official substitutes, while the other ten or so that are sitting in the stands are technically 'reserves'.
"Someteam Reserves" is a name that you will often come across, which refers to a 'second level' team, that (as a team) plays at a lower level, but whose players occasionally 'step up' to the main team when injuries occur.
As I said above, all of this is a little fluid, so I would expect other people can come up with contradictory examples, from other sports or other countries.