There are two or three basis kinds of grease. The most common, and least expensive is lithium based. Good grease. Next is lithium with molybdenum (powdered metal) added to it. It's better, or best for many people and is more expensive than lithium. Then there is a third option that is gaining momentum. It's polyurea grease which is thicker and stickier. It is referred to by,Deere as a best grease and is the most expensive. I like it because it stays put on my loader bucker bucket and makes it less noisy. It's very popular with the industrial crowd I am told. Equally important to the type of grease is the suitability rating it gets and that's printed on the tube. Any of the grease is fine for most of us. Oh, the addition of "moly" to the middle grease makes it particularly nasty from a tracking and removal standpoint of clothes and hands. One little bit will ruin a couch or carpet and it is very difficult to remove from things. The grease may come out but the stain remains. My preferred grease is now Deere polyurea and there are threads around on this. Here's a more complete description from Deere, except it's in reverse order with the "best" first. There are other specialty greases listed but ignore them for now.
John Deere Grease JohnDeere.com Here are grease ratings but 99 percent of us will never need to know other than for conversational purpose.
http://lubromation.com/pdf/CONSISTENCYGRADES.pdf