Why does the air conditioner work in my 1998 Ford Explorer but not the heater. No heat comes out at all when heat is turned on.

Blend door actuator may have failed

That's a very good call Camaro collector, flush heater core / refill / and retest, also check heater control valve for opening and closing under hood on heater hoses passenger side close to firewall, make sure it switches when vacuum is applied

There is probably a vacuum canister somewhere, probably under the hood, which maintains vacuum when accelerating. There is usually a valve on it which can go bad resulting in the problem you are having.

Blend doors that year are electrically actuated

The heater control valve has a vacuum diaphragm to open water passage to the heater- core

They both fail!

Just for information; he wanted to know why A/C worked and not heat. It is like apples and oranges... two separate, individual systems and not connected except for the dash controls. You can't take 1/2 of an apple and orange and join them... doesn't work