Yes, the SAT is slightly harder than the PSAT. Both test the same skills, but the SAT has harder Module 2 content and a 1600 ceiling versus the PSAT's 1520.
The PSAT and SAT test the same skills in the same format. The SAT just extends the difficulty range higher — the hardest SAT questions are harder than the hardest PSAT questions.
A PSAT score is a reasonable predictor of your SAT score if you continue prepping at the same pace. Most students add 30–80 points on the SAT compared to their PSAT thanks to extra practice and content exposure.
Drill free SAT questions by skill, take timed modules, and project your 1600-scale score.