I'm not sure of technical terms, but yes, timothy hay does have different vitamins and minerals in it. For degus timothy hay should be available at all times...As a side note, Alfalfa can be used in a small quantity, but should not be constantly fed. It has too many sugars in it.
There are numerous kinds of hay, some of them specific to certain locales. Most are types of grass mixes. Alfalfa is different though, it is a legume (higher in calcium and protein that most grass hays). Alfalfa is so specialized that it should be rationed for some animals, and excluded from the diet of others, as it is too rich for some.
Straw is pretty devoid nutrients and should only be used for bedding, not for food.
Straw is ok as a bedding material and degus will ingest some of it but its nutrionally no good. Hay is one of the most important parts of a degus diet and a neccessity in order to keep them healthy as it wears the degus teeth down. There are different grades of hay and dried grasses which all work the teeth differently. Timothy hay is one of the best for degus as its high quality and a courser grain so really works the teeth. I feed my degus a mixture of timothy hay, meadow hay and various dried grasses as well as hay cubes and occasionally they will have alfalfa as a treat