The primary difference is that alfalfa is not a grass hay. If you look at it, it's very "clumpy" because it's actually a dried leafy plant instead of a dried grass. It is very high in calcium. Because of this, in most species it's only recommended as a treat or for young animals.
The grass hays have less nutritional differences overall, and are largely interchangeable. A lot of people mix them to give their small animals a variety. Here's a table of all the hays and their various nutritional values:
Most of the grass hays available commercially are either orchardgrass or timothy hay (and they're commonly fed to rabbits, guinea pigs, etc).
We are as gods to the beasts of the fields. We order the time o' their birth and the time o' their death. Between times, we ha' a duty. - Terry Pratchett.
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