Many faucet makers prior to about 1970 made their Bibb washer seats in a “tapered” pattern. The Bibb washer could be either flat or tapered, many would work well with either. The tapered seat pattern did make it a bit easier to regrind the seat face flat since less metal is removed. Remember that Bibb washer globe valve designs require some flat area on the seat or the seat will cut the new washer pretty soon. But if you cut away too much, the seating area will be too wide and you will need a 24” wrench to close it!
A couple of tricks to remember:
Soft Bibb washers, like buna-n have enough “springiness” to actually push the stem and washer back off the seat if the stem is old and the threads worn, or the stem moving through the packing is worn down (packing or o-rings). Consider a hard fiber Bibb washer when you see one do this.
On old two handle shower valves, using tapered (cone-shaped) Bibb washers, especially on the hot side may give the user a finer level of control for shower temperature. The cone-shaped Bibb washer lets the valve mimic the operation of a “characterized” globe valve, with a much wider band of control.