I'm assuming (and you know what they say about that) that hard cast means some type of bullet that is not jacketed, that can be shoot at high speeds so that it won't lead the barrel. Correct?
No not exactly correct.
You basically have four types of bullets. You have the normal cup and core jacketed bullets and the monolytic bullets such as the Barnes X which isn't exactly jacketed since the entire bullet is made of jacket material more or less.
Then you have lead bullets with no jacket and of those there are two types as well soft swaged ones and harder cast bullets. Bullets can be cast of pure lead and are by folks who use them in their muzzle loaders and of nearly pure lead by folks shooting them in BPCRs.
Hard cast is some what of a misnomer really as there is no particular standard as to what is "hard" versus what is not hard. Generally folks refer to bullets considerably harder than pure lead as "hard cast" and that runs the span from wheel weight bullets to linotype bullets. Most commercially cast bullets are VERY HARD closer to linotype in composition than to wheel weights.
Satisfactory bullets can be made for hunting purposes from any alloy from say a 1:30 mix of tin and lead to any combination of lead-tin-antimony you want to use. More tin doesn't add much to hardness but a little tin say up to 2% or so aids in the bullets filling out fully. Antimony is the hardening agent and more is better at making bullets harder up to a point. That point is some thing less than 10% and beyond that point more doesn't do much except make bullets more expensive. About 3% to 6% antimony is a proper amount that makes good hard bullets without adding too much to the cost.
Some water drop bullets made with antimony and arsenic in them to surface harden them but that's really all it does is surface harden them. The hardness is not all the way to the core as it is if they are hard from alloy composition. I do not personally approve of the process. As bullets age they lose that surface hardness and over time will revert to the hardness of the base alloy so starting with a good alloy is to me the key to making good bullets.
Mostly I don't buy cast bullets I either make my own or use jacketed. I use only plain base or gas checked bullets as in my experience bevel base bullets aren't worth my time if I'm wanting to shoot beyond 25 yards or so 50 at the most. Since I don't buy but only use my own I can offer no insight on who to buy from.