How can I tell the difference between a rabbit and a cat?

In Germany we have an old (joking) saying that roughly translates to "head off, tail off - bunny", so your question is legitimate. But first thing's first: There is no health risk¹ involved if you ate the latest shipment of "meowling rabbit".
(To cat lovers everywhere: This is no endorsement, I have a much loved and pampered cat, too!)

The most obvious differences are

• head (look at the teeth!),
• tail (short vs. long), and
• feet (cat claws are quite distinctive).

But I suspect these would be removed prior to sale, so we'd have to dig a bit deeper into anatomy:

• Shoulder blades:
  Cats' shoulder blades are rounded on top, especially in the front, making the shoulder blade almost semicircular with the ridge making for two differently shaped parts, rabbits' shoulder blades are triangular with the ridge somewhat parallel to the front side.

• Femur (thigh bone):
  A cat's femora are straight, whereas a rabbit's is more or less bent, especially pronounced in older animals. Same applies to a lesser extent to radius and ulna (forearm), but they might have been removed.

• Ribs:
  Cats' ribs are "rounder" than rabbits' ribs according to this source. I can't say by how much, but @aitchnyu's comment below suggests the difference is obvious enough to play a significant role in the novel/movie Papillon.

• Pelvis:
  The same source as above states that the foramen obturatum (= the loop-like opening near/below the hip joint) is oval in rabbits and round in cats. I couldn't find a good picture to show this, though.

Here's a rabbit:

Source: www.onlineveterinaryanatomy.net

And a cat:

¹ other than the general risk every meat from questionable sources brings

In the textbook Text-book of meat hygiene: with special consideration to ante-mortem and post-mortem inspection of food-producing animals (Edelmann & Eichorn, 1908), pages 64-65 concern determining the difference between a cat and rabbit:

The following differences in the skeleton are especially to be mentioned: The lateral processes of the lumbar vertebrae which are directed forward terminate in the rabbit (Fig. 34) in two extensions, of which one is directed forward the other backward; in the cat they terminate in a point. The body of the first three lumbar vertebrae in the rabbit contains thorn-shaped ventral processes (Fig. 34 a). The ribs of the rabbit are flat and broad; those of the cat are rounded. On the scapula of the rabbit the acromion turns around posteriorly and terminates in a long point, which is directed backward (Fig. 37)). Radius and ulna are completely separated in the cat (Fig. 35); in the Leporides they are united (Fig. 36). On the humerus of the cat is an elongated fissure over the median condyle of the distal end (Fig. 39). The femur of the rabbit (Fig. 41) contains below the trochanter major, a specially strong smaller trochanter, which is absent in the cat. Tibia and fibula are complete in the cat (Fig. 43); in the rabbit (Fig. 44) they are only separated in the upper half.

The whoe carcass of the cat can be immediately recognized by its head, penis bone, and the tail, and for these reasons, if offered for sale, these parts are always removed on the slaughtered animal. Rabbits generally have the shot wounds, but these are naturally absent in the slaughtered domesticated rabbits. The meat of the cat is paler than rabbit meat; the fat of the cat appears whitish in contrast to rabbit fat, which is honey-yellow.

As it says, it has some explicit figures which you can go and see, showing the different bones of the one next to the corresponding bone in the other, so that you can easily see the differences.

If you don't speak anatomy, let me translate. See also the image below.

This is a 1908 book that tells food inspectors how to tell when someone is selling cats as hares/rabbits. They say that, for a true rabbit:

1. the fat will be faintly yellowish rather than white;
2. the forward-spikes of the vertebrae in the spine should sometimes have a subtle Y shape near their ends, ending in a little "prong";
3. the ribs will be noticeably flat-and-broad rather than rounded;
4. there will be a little spike on the shoulder-blade near the forelimb;
5. when you look at either cat or rabbit, both the fore- and hind-limbs, like our arms and legs, have an upper-arm/thigh with one big bone (humerus/femur) and a lower-arm/calf with two smaller bones (radius+ulna/fibia+tibia): in the rabbit both of these lower-two-bones are fused close together on both fore- and hind-limbs, whereas in the cat they're noticeably separate bones;
6. there should be a little hole in the upper-arm bone (humerus) right above the elbow; and
7. on the side of the "thigh" bone where there's a "ball" connecting to the hips, you should also see beneath the biggest "lump" across from the "ball" a lesser "lump" coming after it.

How will you see these? To look at the bones you can probably just stew one of the animals pretty hard until the meat is "just falling off the bone," then carefully pick the meat off.

Make sure before you use any of these criteria to conclude catness that you have seen the difference on between two images of skeletons. Sometimes the difference is rather subtle! For example in the images that Stephie has posted, you can very easily see the "shoulder-blade spike" (labeled #33) on the rabbit, but not on the cat, so this is a clear diagnostic criterion: if I didn't see it then I'd strongly suspect "cat". Similarly the fused/unfused bones are pretty decisive, as long as you don't accidentally remove the incredibly-thin tibia of the cat and then think "oh, I just see one bone, it must be fused." Be cautious until you compare to both.

I've taken an image from Flickr and updated it with some highlights of what this 1908 manual is suggesting you look for:

The simplest way to tell the difference is to look at the ribs.

Cats have one pair of floating ribs, but rabbits have three pairs. The floating ribs are the ones at the bottom (i.e. towards the tail), that are not attached to anything at their outer end. All the other ribs are either attached directly to the breastbone, or to the cartilage that extends from the base of the breastbone.

Cats have nine "true" ribs (attached directly to the breastbone), three "false" ribs (attached to the cartilage), and one pair of floating ribs. Rabbits have seven "true", two "false", and three floating. So cats have a total of thirteen ribs, but rabbits typically only have twelve (although it can vary).

This gives us a simple test:

• if it only has twelve ribs, it's a rabbit
• if it has thirteen ribs, but only one pair of floating ribs, it's a cat

The easy way is to look at skull, paws, and tail - but these are normally removed!

Cat have short paws, long tails, and a sleeker skull

Hares have very long rear legs, easy to spot

Rabbit have curved lower leg bones (tibia and radius?), shaped like this ()

Cats generally have quite straight lower leg bones, shaped like this V. The are nearly touching each other

The main differences I see in the skeletons of the two animals is that the cat's humerus (large single bone in the front legs) and its radius/ulna (smaller dual bones in the front legs) seem to be very close in length, or the single bone is slightly longer. The same goes for the hind legs, where the femur (single bone) and the tibia/fibula (dual bones) are of similar length or the single bone is slightly longer.

In the rabbit, the dual bones (radius/ulna in front leg and tibia/fibula in hind leg) are significantly and very noticeably longer than the single bones (humerus and femur, respectively). This is more evident in the hind legs, where the tibia/fibula combo seems to be about 20-30% longer than the femur.

As a child in the 1940's we were told that you could tell the difference between a skinned cat and a rabbit because one of them had kidneys side by side and the other's kidneys were staggered. I think the rabbits were side by side because they tasted delicious.