Hmm ... it sounds like your can changes grit depending on which side you are facing!
I would venture to guess that probably what you have is relatively coarse. I should note that I am very much a newbie, with much to learn! But as I understand it, valve grinding compound for automotive use tends to be coarser than what may be needed for model engine use.
I'm aware of at least a couple of different approaches to getting different grits. Some buy the grits as a dry powder, then add in oil to make a paste to use in grinding. The powder can be diamond, silicone carbide, maybe also aluminum oxide; I don't know enough to know the advantages or disadvantages of each, though I have seen the sentiment that "diamonds are forever" and that is
not a good thing - you don't want the grit to continue to grind once you are done lapping!
The other approach is to buy the grinding compound already mixed up as a paste - probably similar to what you now have. I went this route via eBay. Sometimes the ads just say "valve grinding compound" without specifying a grit, but with a little digging I was able to find listings for different grits. As I recall, it wasn't overly expensive, and using them for model engines, the containers I received will probably last the rest of my life.
I am under the impression that what I found is silicone carbide as far as the grit, but I'm not entirely sure - I'll have to go back and look at the containers to see if they say.