Yes, I know: "Remember, there are no stupid questions, only stupid people." - Mr Garrison (South Park).
Okay, I've been thinking about this for a while now and I don't have ANY answer, much less a good one, so I'd like to hear what you have to say about it.
Once upon a time, long ago (some longer than others), you picked up a guitar and had no idea what to do with it. You decided that you wanted to learn how to play it, so you began lessons (formal or informal), or began teaching yourself some basics, such as picking out songs note by note. Eventually you learned your first chord. And then another, and then maybe a third or fourth. Pretty soon, you learned a basic strumming pattern and learned how to make your fretting hand change from chord to chord faster and faster. You kept practicing, and eventually maybe you learned how to play your first "song".
Later, you learned more chords, different strumming patterns, and eventually maybe some fingerpicking patterns as well. Your skills and dexterity increased along with your knowledge. The more you practiced, the better you got (except for that darned B7 chord, which you're convinced was first proposed by Satan).
Eventually, YOU GOT TO THE POINT where if anyone asked, you could say that you "play the guitar" and you can call yourself a "guitar player".
Here's my question: WHAT IS THAT POINT?
In other words, at what point did you consider yourself transitioning from playing AROUND on a guitar to PLAYING a guitar?
I do realize that skill levels vary greatly from person to person. A year or so ago, I considered my brother-in-law to be a "good" guitar player. During this past year, I've pretty much caught up with him, but when I ask myself: "Am I a guitar player?", I still consider myself to be an amateur who is not very good. So I don't know if I can consider myself a guitar player, or whether I'm still just playing around.
I was trying to liken it to a sports analogy. I used to play baseball. When I played on a TEAM, I considered myself to be a baseball player. Now that I'm no longer on a team, I no longer consider myself to be a baseball player, even though I still know how to play. By that analogy, I'm not a guitar player unless I'm in a band, which is definitely not true. You can see why that analogy doesn't work.
Truth be told, it's really not that important. But what tickled my brain on this was that recently I was at a function and the subject of guitars came up. Some on asked me: "Do you play?", and all I could muster was "Well, sort of." I would like to be able to answer that question with: "DANG STRAIGHT! BRING IT!"
(By this point, you're probably thinking: This guy thinks about things too much. And you'd probably be right.)
So here it is - For those of you who DO consider yourselves to be guitar players: At what point did you realize that you are one?
(Now you understand the title of this post.) 
Thanks for indulging,
'Nomikal
