Studying for the ACT but taking the SAT?

I’m really familiar with the ACT and have prepared extensively for it. I got a 33 in the April ACT. If I’m prepared for the ACT, can I apply that preparation for the SAT? I got a 35 on the ACT English section, so my grammar is quite strong. However, the ACT doesn’t test vocabulary, and I know the SAT does. Also, I believe the math section is actually a bit easier in the SAT compared to ACT. Do you think I should take the SAT in May? How should I go about preparing?