We usually see elephant seals hauled out on the beach for fighting, mating, giving birth and nursing. Both males and females fast during this entire period, losing about a third of their body weight. But when they go out to sea to hunt and build up reserves for next season's haul out, the males and females split up.
Males go north to hunting grounds off Alaska, and tend to dive straight to the bottom to catch their prey. That means they're more likely to eat an octopus than a squid, since octopuses are bottom-dwellers while squid swim up in the middle of the water.
Females, meanwhile, go far out to sea, diving deep but not to the bottom, catching their prey from the water column. They are the ones chowing down on midwater squid.
If you find yourself along the central California coast, you can check out the elephant seal rookery at Piedras Blancas, where there are some lovely new interpretative signs, including a painting of a female elephant seal hunting squid!
(The squid are mostly anatomically correct, except they are missing fins. Easier for Ms. Seal to catch, I suppose.)