In the recommender systems section of his famous Coursera machine learning course, when Andrew Ng wants to introduce collaborative filtering, he says that each movie has some features and each user has some parameters. Why he distinguishes between users and movies aspects? I think we can say that as the features of the users and the features of the movies.
Most collaborative filtering models define the affinity of user $i$ toward product $j$ as $u_i^Tv_j$, where $u_i$ is the preference (or parameter) vector of the user and and $v_j$ is the feature vector of the item. Note that these tend to be abstractions, because collaborative filtering algorithms need to do a minimization to even find these vectors $u,v$.
Both vectors live in a vector space of the same dimension, but we typically distinguish the two because one vector captures the user's likes and hates, wheras $v$ captures abstract features of the movie that translate to likes or hates when inner-producted with a given user.