My .02 cents worth. A couple of generalized characteristics. Aloe - "teeth" on leaf edges, smooth leaves. Haworthias - ?
Gasterias - some have bumpy, rough textured leaves, others rounded leaf ends. Good luck.

You rarely see them in bloom at the store, but Gasteria have a bulge at the base of the flower. Haworthia flowers are almost always small, white, and have green markings. Time and experience will help you recognize some differences, but so many hybrids can blur the lines between the 3 genera.

Another distinguishing characteriastic (at least for some Gasterias) is the pattern of growing in only a pair leaves or what looks like a vertically stacked pair of leaves. I don't know how to pronunce this, but I think that habit is referred to as distichious (growing in pairs?)

Aloes tend to grow more in rosettes, some on stems, some not; Haworthias also tend to be rosettes or in clumps or clusters of rosettes. Gasterias can do that too, but not necessarily. Does that help somewhat?

Perhaps spend some time at Desert-tropicals.com, which will allow you to see pix of many varieties of each of the 3 plants, that should give you an idea of the types of varities & forms btwn these 3 species.

Some Haworthia, do have teeth, fine hairs, spots, windows on tips, Gasteria are larger smoother, mostly, leaves with spots. Many good books on the three species. Many of these will color up also with good sun.

Haworthia, mostly clumps, some have soft teeth, all colors of leaves in good sun. Leaf will grow to a tip and not rounded on most species. Too many to give you a run down.
Aloe can grow into trees, singles, some clump. Aloe flowers are very colorful, red ,yellow, variegated. Some are branched, or spikes, too many species to give you a run down.
Howorthia flowers usually white, one or two are pink, with small soft leaves full of water, many you can see through when held up to the sun light. Most can be grown in a small 4" pot all of their life. Either 3-4 have a perfume smell to the flower.

Aloe most cannot be grown in small pots, only a few.

Gasteria most must have at least a 8" pot, a few can do well in a 4" pot, if you know what you are doing. Mine are all dormant at this time of year, Gasteria and Haworthia, will appreciate some shade this time of year, and they like to be kept cool, they are dormant. They will start to grow new roots when it gets cool here in October.

Gasteria have them hanging down, usually red/orange with perhaps yellow on the ends. This information is only added information that might be useful, there are books writen on each of these species. This is meant to be only a brief idea of each species. Norma

The link below is an excellent resource with pictures of Gasteria species. Many of the Gasteria you encounter will be hybrids, but study the pictures to get a feel for what Gasteria can look like.

Here is a link that might be useful: Gasteria.org pictures and descriptions