flummoxed: I'm pretty sure I'd qualify as a collector, but I'm trying to make an effort to play every single game in my catalog. Out of about 400 games I've played only 60-70, but I'm getting there :D
I'd self-identify as a gamer insofar as I enjoy video games and I have a lot of them and play fairly regularly. I've got probably around 1000 games if I include GOG, Steam, as well as direct-download games from GMG, GG, Shinyloot, Desura, various bundle sites, and CD/DVD based games, but I wouldn't really call myself a collector as my goal is not to acquire and collect them for the sake of collection. So I'd have to say I'm a gamer in that regard.
The majority of games I've actually bought or gotten from gifts, giveaways, free promos etc. are all games I'd like to play over time but there are so many it may not be realistic to expect to get to them all. So I wouldn't say it is a goal to play or complete them all as that doesn't really matter to me. I simply play games for entertainment, whether it is one or 20 over a given period of time and as long as I enjoy what I'm doing then they have served me well.
If I were to feel I need to play them all and play them as if they were a queue of work that I'm obligated to complete then that wouldn't exactly be fun or entertaining per se and would be more of a mountainous burden than an enjoyable hobby/interest. I consider my library of games to be like a private version of a public library, where I have a variety of experiences I can opt into, and I simply choose which of them I wish to experience at a given time with no feeling of obligation to complete them all. The list of available games in the library grows faster than my rate of playing them, so attempting to play them all would be a losing battle and possibly miss out on other important things in life ending up being a slave to the games.
In other words - Do you own your games, or do your games own you?
That's a twist on a line from Fight Club pertaining to material possessions, of which games are. I prefer them to be a chosen entertaining distraction rather than a mountain of goals to complete.