I would expect
/v1/users/123/messages
to return all the messages that belongs to this user. This means received, sent, deleted, tagged, drafted etc.
To specify a subset of a resource you can go two ways with this like you and bertvh stated:
Querystring: I find it perfectly valid for filtering as e.g.
/v1/users/123/messages?type=received&folder=important
Or as a subresource: Use this if you expect to have a lot of filter options on a higher level e.g.
/v1/users/123/messages/received?folder=important
As you can see this would reduce a filter option.
And like bertvh stated, the underlying database schema is irrelevant for serving the responses.