I give my sheep and horses whatever I get hold of, but they only have it in winter. I have my own haylage so they usually end up with that, haylage is richer than dry hay though as it's baled earlier so that there is more moisture and nutrients still in the grass. Both my horses and sheep are fine on it.
Silage = grass that is cut and baled immediately, usually very wet and cut early in the year. Not very suitable for horses or sheep due to the risk of botulism and rich content.
Haylage = grass that has been cut and left to dry for a few days, ideally turned before baling and wrapping but sometimes it's not. Usually cut later in the year than silage, and the nutritional content depends upon the type of grass. Some haylage can be borderline silage if the weather hasn't allowed it to dry. The baling stops the fermenting process but once a bale is opened then the fermenting starts again and a bale of haylage will have to be used within a period of time to stop it becoming mouldy. Okay for horses and sheep but not ideal for native ponies and good doers!
Hay = cut grass that has been turned several times to totally dry out (sometimes very hard to predict when this can be as it all depends on the weather!). Ideally needs a dry spell up to a week before baling. Nutrients vary depending on type of grass and when baled (the later it's baled the less nutrients are in it).
Hay can vary tremendously in quality but generally it's easy to spot good quality stuff, it will be a bit green and smell sweet whereas bad quality will be yellow, dry and dusty and not smell nice. Hay can harbour a lot of mould spores too, much more than haylage, unless the haylage has gone off!