These things get referred to in different ways in different areas. Where I am, a “balancer” will have the vitamins and minerals, but also extra protein. A “vitamin-mineral supplement” will not have the added protein, usually just the vitamins and minerals in some sort of carrier. Here is what I use for my mare; she gets 1/2 cup per day. This one actually does have some protein from the alfalfa carrier; I tried the somewhat less expensive and less caloric powder form, but my mare would not eat it.
“Equalizer” is a product name - it’s Seminole’s ration balancer for grass-based diets.
Seminole Grass Balancer is in the category of “forage balancer”, like California Trace, Vermont Blend, Arizona Copper Complete, Lone Star Trace, and some others. It has a few of the more commonly needed nutrients, so not nearly as comprehensive as ration balancers. Some forage balancers are more comprehensive than this one, some a bit less.
Saying “look for a grass balancer” means to most people things like Triple Crown Balancer or Balancer Gold, Purina Enrich, Nutrena Empower Balance, etc - the equivalents of Seminole Equalizer
Looking for a “forage balancer” is going to find a lot more useful products for what you are actually intending.