No, a standing rib roast, also known as prime rib, is a much
better cut of meat and comes from an area just to the rear of the
cross rib roast, also known as English roast. The cross rib roast
is from the cut of beef known as "chuck", which is from the top of
the forelimb, near where it meets the shoulder blades. The standing
rib roast comes from the area of the ribs where they meet the rib
cage (above the area of the rib cage where the "short plate" cut
is). They really are not the same, and do not cook the same way.
The cross rib roast is best braised, whereas the standing rib roast
is best roasted. You should see a difference in the price, with
cross rib roast being less expensive than standing rib roast.