A format crossover is a specific type of crossover between two series consisting in a fictional work that only features in-universe elements from one of them, and the general format from the other.

The format crossover is still considered part of both series, therefore being a direct crossover, but it's exceptionally a type 3 link rather than a type 1 link, since elements from the two series' universes don't directly interact.

An example is Dance Dance Revolution: Mario Mix, that while titled both "Dance Dance Revolution" and "Mario" and therefore being considered a crossover, part of both series, an inspection on the game's content shows that it only features elements from the Mario universe, and only the gameplay from the Dance Dance Revolution series, so it's a format crossover: it's a Mario game created using the "format" from the Dance Dance Revolution series.

It should be noted that format crossovers are still considered type 1 links by some people though, since even if they feature elements from only one game's universe, they can still be considered an entry in the other series' multiverse (for example the events in Dance Dance Revolution: Mario Mix can be considered taking place in an alternate "Dance Dance Revolution" universe, part of the same multiverse), so this is quite an arguable topic overall.