The most important thing you need to understand is that a vanilla option, no matter it is a call or put, always has positive gamma. That means if you buy options you benefit from the increase of volatility and suffers from time decay. In my mind, managing gamma is the key to trade options. Directional movement is secondary.
The phrase "option sellers" usually refers to people who write options, not people who sell an option they previously purchased. If I buy a call option and then decide I don't want it later so I sell it, I wouldn't say I'm an "option seller." I mean technically I did just sell an option, but I don't think that's what it usually means. If you're doing like covered calls or something it's probably less confusing to just say "I'm going to write an option."
The counter-party has no idea (unless prearranged) that a write isn't a sell to close. You can only buy or sell an option. There is no gains to be had by delving into semantics. You can sell (short) an option to open a position. There is a margin req as the risk is greater than the reward. You can spread (buy a call, sell another call) or trade combinations (buying and selling of calls and puts).