The complete, correct term for the bullet you are describing is lead conical. There are others.
https://www.muzzle-loaders.com/bullets/thor-bullet-full-bore-conical-300-grain-1430.html
The Complete Black Powder Handbook refers to copper conicals.
Powerbelts are technically conicals, too, although it's an unusual, composite version (the hollow based of the cone is made from the plastic skirt, but it serves exactly the same purpose as the hollow base of a lead conical).
Conical describes a shape, not a metalurgy. Because, once upon a time, all conical BP bullets were made from lead, the shorthand is to think of all conicals as lead, but it's technically innacurate.
Here's how Cabelas BP projectiles page states it:
Conical bullets have been around for a long time. Usually made from pure lead, like balls, most have a hollow base that allows them to "upset" and grip the rifling.
I highlighted the important word relative to our discussion.
http://www.cabelas.com/product/Your-Guide-to-Muzzleloader-Bullets/531669.uts
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I'll take your word for it.
For the 35 years I have been a BP shooter, the terminology I used is accurate. I have no idea what today's BP online youtubers are using. Traditionally, there are round balls, conicals, and minie ball bullets . All should be pure lead.
the reason for specifying pure lead NON jacketed bullets is because you have to cut the rifling into the bullet as you load it down the barrel. You will never accomplish this with a jacketed projectile, and is why discarding sabot loads came about for firing jacketed bullets. The only way to load a jacketed bullet in a ML is to use a undersize bullet. Poor performance and poor accuracy is the result of this.
Cabellas is not known for their expertise, you might try "Track Of The Wolf" if you are interested in the subject.
"Conical bullets have been around for a long time. Usually from pure lead, like balls, most have a hollow base that allows them to "upset" and grip the rifling"
This refers to the minie ball that was used during the war of Northern Aggression. The main reason for it was to allow loading of a fouled barrel, as cleaning the gun was not normal during a firefight. The Minié ball, or Minie ball, is a type of muzzle-loading spin-stabilized rifle bullet named after its co-developer, Claude-Étienne Minié, inventor of the Minié rifle. It came to prominence in the Crimean War and American Civil War.
The minie is rarely used for hunting today.