If it really was an "inheritance" tax, then each person would have an "inheritance tax allowance", that is the amount they are allowed to inherit before the taxes start. So if 20 of my ancestors all kicked the bucket at once, each leaving me a modest fortune that adds up to a large total, then I would be liable for a hefty inheritance tax bill. Whereas, if great aunt Mabel died and left $1000 for each of her 1000 progeny, then no tax would be due, as surely a measly sum like $1000 would fall below any reasonable inheritance limit.
The "death" or "estate" tax is levied on the value of the assets of the person who died, not on the value of the amount received by an individual who inherits. Ergo, it's a death tax.