Premier Access refers to a number of extra benefits United offers elites and credit card holders, like special check-in desks, priority screening, priority baggage off-loading, and priority boarding. Presidential Plus is a now-discontinued Chase co-branded credit card that I'm assuming you still hold.
FWIW, my club card says Premier Access and then, below it, Mileage Plus Club Card (the credit card I hold). Neither matter much, though, because since the club now requires a same-day boarding pass for entry even if you hold a membership, I simply scan my boarding pass for access. Presumably, I'd need my membership card if I held a boarding pass for a different airline, though 99% of my flying is UA. I'd also need the card to access Star Alliance lounges, though 99% of my flying is domestic.