If you are organized / taxed as an S-Corp, then the 25% employer-side is of your W-2 earnings, not of your total profits.
Otherwise I think you've got it.
If you are a sole-proprietor, then your employer limit is 20% of your net, less 1/2 self-employment taxes. To save some head-scratching, this is equivalent to an S-Corp where you bonus yourself out so that you've got exactly 0 "profits" at year end.
So long story short, how you choose to organize doesn't effect your Solo401K contribution limits. Except if you go S-Corp, you're likely doing so so that you can pay yourself a lower salary than the total profits of the business and so save on self-employment taxes. Since in that case, you're lowering your W-2 from what you could do, that would lower your Solo401K limits. But that isn't because you're an S-Corp, it is because of how you choose to compensate yourself from said S-Corp.
And it really doesn't matter where the money comes from either. You'd probably want to pay everything from your business account for organization purposes, but you don't have to have a separate business checking account.