I haven't taken any of the IE courses by SQLSkills so couldn't compare what is actually on the slides and the context.

But from what you posted it looks like the same thing is being said - just in a different way.

Both reference the hash being a two phase operation. Both statements reference the hash table as the first table being built (which is the top table in the execution plan) and the second table being the bottom input from the plan and that it probes the first table (in other words probes the hash table that was built from the top input).

First and second table are according to the execution plan and not the order you had them listed in your query.