"Standard" plywood in the US is generally made of softwood plies, and may or may not have a thin hardwood veneer on one or both sides - so-called "maple", "oak", etc. plywood you see in many hardware stores and home centers. I believe that is the kind of plywood EZ-Lok is referring to. The veneer is simply for appearance, and doesn't do much of anything for the strength of the product.
On the other hand, as you mention, Baltic Birch and the similar American Birch plywood products are made with birch through and through, and so would classify as a hardwood. Their fine thread inserts should work well in these sheets. That being said, unless your inserts are going to be subject to extraordinary loads, the coarse threaded inserts should be fine as well. I have been known to use coarse-thread wood screws in hardwood when fine-thread ones weren't available, and I've never had an issue with them. If you are putting the inserts into thinner sheets of plywood, the higher thread count of the finely-threaded inserts may be desirable, but in many cases coarse will be sufficient. Without more details on the dimensions, it's difficult to give more specific advice, but my gut feeling is that either will work here. For utmost peace of mind, though, go with fine. It certainly won't detract from the strength of the connection.