I always say a star and a flat screwdriver but Phillips is correct. Not 100% sure if the other one is correct or not but it sounds right. 😅

Yes. Flat head (or slotted head) screwdriver and a phillips screwdriver

"Phillips" is an American term, therefore other countries often use the generic term "crosshead". Also, this type are often mistaken for the very similar "posidrive" head.

In the States we say a standard screwdriver and a phillips screwdriver. A star tipped driver usually has 5 or 6 tips on the blade. Pretty easy to search on the internet.