I want to place an electric stove where my dryer is now located? Is the same outlet used for both?

That would depend on the # of amps used.If the amps are the same then the plug would be same. Even with the amps the same there may be a small difference plugs but the wire would be the same.

be sure that the breaker is off when working on the outlet.

Chuck

A standard dryer is a 30 amp circuit, an a range is 40. No, you cannot use the dryer outlet or circuit for a range. A new circuit, to include #8 cable, a 40 amp circuit breaker, and a 40 amp receptacle is needed.