The entire value of redis IMO is that is ISN'T inside your normal application, but rather some shared storage that all nodes can use to coordinate and that survives deploys, but that provides more ergonomic data structures than SQL databases. Caches are only one type of such shared data, but things like feature flags, circuit breakers and rate limiters are also super common (and super useful).
However, Mnesia seems like it is quite a bit more of a complete distributed database engine than Redis. To me the nicest thing about Redis is just the convenience of what it offers: very fast data structures, serialized, optimized (at least by default) for cases where speed is more important than durability. It is simple on many levels and somewhat constrained in scope. Mnesia seems to be aiming more generally in the distributed database category.
So how do you feel they compare?