I got really into cocktails a few years ago (or "mixed drinks", if you want to be more technically correct). No way I'd be able to keep up at a real bar, even if I probably know more cocktails than many of the bartenders I've personally interacted with (TBF I haven't been to a bar since I really got into cocktails, and before I got into it I just went wherever it was cheap). Fixing drinks is at best half of the job anyway, and I'm rubbish at the people stuff.
"Cocktail" is more specific. Originally, it was identical with what's now called an Old Fashioned, i.e. spirit, sugar, bitters and water/ice. Later the term started including other alcoholic drinks like sours, martini etc.; I've seen people claim in discussions that's it's down to the amount of ingredients (e.g. a Rum & Coke is not a cocktail, but rum, cola and lime (Cuba Libre) might be) or a specific care exercized in preparation, but I think it's ultimately arbitrary.
Anyway, one of my favourite drinks is the Twice Up (whisky and water mixed 1:1, works great with many other spirits). Hard to call this a cocktail, considering adding water to whisky is just a completely normal way of drinking whisky in Scotland. The Scots just pour the water freehand instead of measuring an exact amount.