Simple sentence x Compound sentence

Hello guys! I was doing an online exercise about simple and compound sentences. The website told me two sentences I corrected were wrong.

"The basketball tickets are expensive, and we don't have much money to spend." (I put a comma before the conjunction)

"We ran to the end of the street and crossed to the other side." (I didn't put a comma before the conjunction because it's a simple sentence with compound verb so no need to do so)

Can someone explain me why? Isn't the first sentence a compound sentence and thus I have to use a comma? And the second sentence shouldn't have a comma because it's a compound verb?