There is more then one type of hay. They have different nutrition and taste to your herbivore. Just like dog and cat foods, you can use different hays for different life stages and body types.
Lets start with what first and second cutting means.
First cutting hay is the first hay of the season. Generally more course and stemmy, with a higher fiber and lower protein content. There may also be more weeds in first cutting hay. This hay may be less palatable then second cutting hays. This hay though, would be a good choice for an overweight adult herbivore.
Second cutting hay, is usually cut 45-60 days after the fist cutting. The stems are finer, softer, and sweeter. This hay is higher in protein and lower in fiber. This is an ideal cut for most rabbits.
There can be third and even fourth cut hays in places with long growing seasons. This hay is usually too rich and low in fiber to be used as a main diet for most rabbits. It can be useful for growing animals, or animals with higher nutritional needs.
Now we know what the different cutting mean, we can look at actual hay types.
Alfalfa, is not a grass, but a legume. It is really very high in protein, and low in fiber. Its also pretty high in calcium. This is not at all good for a typical rabbit or guinea pig. It can be fed to growing animals however.
Timothy hay, this is the most common type of hay, and the most recommended. Timothy hay makes a great staple, main diet for the average rabbit or guinea pig. Is is soft, leafy, green, and has a great protein to fiber ratio.
Orchard grass, and brome are other hays that are similar timothy. Good choices as well, and can be fed as a primary hay or mixed with other hays for variety. Soft leafy green hays.
Oat hay, is a very high in fiber, crunchy, stemmy hay. This is a good choice for overweight rabbits and guinea pigs. It is not rich ata ll, lower in protein and higher in fiber. This hay is great for animals prone to stasis as well.
Botanical, or herbal hays, are any type of hay with aromatic herbs added. Usually chamomile, dandelion, or lavender are added. Great choice for picky eaters or rabbits that are not eating well. Its a really good treat hay too.
Hopefully this helps you pick out your next bag or bale of hay.