I don't give a shit about esports, livestreaming, or any of that newfangled nonsense.
By "competitive play" I simply mean teams of skilled, organized players fighting it out, who would almost certainly cream any batch of randoms in a pubbie match. This sort of competitive team play existed long before anyone thought of video games as "sports" and spectators are unnecessary, although I suppose now that esports are a thing, private team play might be the equivalent of local or regional baseball teams competing with each other.
In general, public twitch shooter players (AKA pubbies) queue up for random or matchmade public matches (or join a server, etc.), just as the average dota player does in LoL or Dota 2, and that's their entire gameplay. Competitive players most likely began as pubbies, or perhaps migrated from a similar game in the genre, but at some point in time (possibly from the start) began taking their learning process more seriously, analytically, and self-critically (rather than simply experientially) with an eye toward joining or forming a competitive team, practicing as part of a team following team strategies and doctrines, and competing against other teams (as opposed to having random allies and enemies as the winds blow).
The exact differences between a pubbie and a comp player are a bit hard to explain, actually. There are plenty of pubbie players who could destroy a comp player in a 1 vs. 1 deathmatch, for example, but team play is about much more than 1 vs. 1 duels, as anyone familiar with world history ought to know.
The point is, all professional esports are competitive play, but not all competitive play is professional esports.
