Well, the previous comment was describing the use of Redis as a cache, and in that use case, yeah, it's kind of between the application and the database.
That said, caching is just one of the possible uses for Redis. I think of it as an easy way to share arrays, dictionaries, queues, etc between different applications. Then it's easy to see how it can be used for almost anything.
When used as a cache, Redis is often used as a 'look aside cache' (vs 'look thru cache'). Generally speaking, Redis does not talk directly to your database. Instead, your code looks to Redis, and then if it doesn't find what it's looking for, your code looks to your SQL database
Also, where does Redis sit (my guess is between request & database)?