Ok, ill take a shot at this, having owned/operated/managed an online gaming "Clan" for 9+ years now.
As stated before a Clan is pretty much the same thing as a Guild. I would equate a "Pirates Clan" to being your standard POTCO guild.
In my case, my "Clan" aka Old Farts eXtreme (OFX) has been a circle of friends, which has definately changed over time as members interests varied... that play online games together. People that share the same gaming styles, get along together etc.
Our clan was formed long ago because we were tired of playing games with adolescents that constantly found it necessary to practice using the new 4 letter words they'd learned, boast about thier gaming prowess (usually achieved through using some autoaim/wallhack cheat), etc. We wanted a circle of people we trusted to be fair, not to cheat, had similar interests, and were of similar age (we had a rule of 30yrs old or older ONLY in our clan... although we've loosened that up over the years).
The term "Guild" to me is actually the new term, which to me is associated with MMORG games. But it serves a similar purpose. In most online gaming they are used like "team" designations... showing your colors.
As a "Clan" my group has competed on various gaming ladders.. ok, ready.. this will date me..
We started with "Duke Nukem 3d" LOL ancient history....
Moved to quake 2, then quake 3, then Counterstrike source. (all online shooters).
Now we actually specialize in online racing (rFactor, with multiple mods covering various racing disciplines) with only a few of us interested in POTCO. Matter of fact, I am currently on vacation at our 3rd annual Clan get together at the NASCAR All Star race in Charlotte, NC (OFx's from all over the US attend).
The actual term "Clan" is associated with Family... often used in early european culture. Scottish decendants will often speak of the "Clan" of thier ancestory.
Zeppers lvl40
http://pirates.teamofx.us <-- Foul Windbags "Guild" site (Disney wouldnt allow "Old Farts")
http://www.teamofx.net <-- Current Clan website
http://www.ofxgamer.com <-- Old Clan website