This wiki is incomplete.
The theta of an option is the sensitivity of the option to time.
By convention, theta is negative, which means that if you are long an option, it loses value over time.
It is better to say "paying theta" or "collecting theta" to be more explicit about the position. This is because while being long options means that you are paying theta, it is possible to be long an option strategy (like butterfly or calander spreads) and be collecting theta.
From Put-Call Parity, . There is a very small difference of , which is often considered negligible.