The traditional bottle cap is simple known as a crown cap or crown cork, and there was a time when simply saying bottle cap indicated a crown cap which invariably required a church key or similar tool to remove.
But just as the advent of the push-button telephone requires us to specify rotary phone, and of the mobile phone to say land line or home phone instead of just phone, the popularity of twist-off bottle caps has led the rise of the term pry-off or pry caps among beer enthusiasts. Googling around you will find it in widespread use on homebrew sites, and it used by at least a few brewers as well. By synechdoche, a twist-off can refer to a bottle capped with a twist-off cap, or the sort of brew sold in such bottles.
Twist-off bottle caps are easier to open, but more complicated to manufacture and, it is claimed, an inferior seal. They were therefore adopted primarily for mass market, mass consumption brews— the Coca-Colas and Heinekens and Budweisers of the world. Smaller bottlers would not have found the need to invest in the machinery for twist-off caps, and this has even become a point of differentiation among craft brewers.
In North America, I've almost never heard the term screw cap or screw top applied to crown cap bottles like beer bottles; for beverages they refer mainly to the type of metal cap found on Australian wines, with similar mass market associations.