If you sell an option it has positive theta, so you collect theta over the life of the option. If you buy an option, it has negative theta which works against you as your option is worth less as it decays.
No. You conflate
option theta with
time value. Speed versus speed*time=distance.
Option theta is the rate at which an option loses market value due to the passage of time. Option theta, discounting time travel effects, is always a negative number.
Option theta is not something that gets "collected" -- it is a rate-of-change.
Time value may be usefully thought of as "collected", via the passage of time, through the application of theta.
How option theta affects your position and/or your account is a different matter, and in simple trades is as your post suggests -- (net) long positions lose time value, (net) short positions gain time value.
FWIW, option theta -- as a rate-of-change given a passage of time -- may be usefully summed over any number of positions
and over any number of underlying contracts or any number of markets. (The basis is time!) Thus, summing the rates-of-change for an entire portfolio for a given day can be a *very* useful guidepost to portfolio construction or trade management requirements. In doing so, you have just calculated the net effect of the time value impact, for that day. Sweet, right?