# Are there two distinctly separate definitions for the Optional Stopping Theorem?

I have been reading a book called Stochastic Calculus by Steele. Inside, they have a theorem they state as the "Optional Stopping Time Theorem":

If $M_n$ is a martingale with respect to $\mathcal{F}_n$, then the stopped process $M_{n \wedge \tau}$ is also a martingale with respect to $\mathcal{F}_n$.

However, on Wikipedia, Optional Stopping Theorem - Wikipedia they state the optional stopping theorem in terms of three separate sufficient statements. At first glance, these two don't look the same. Is there a chance they are talking about the same thing?