If a stopper does not lift straight out, it is being held in by the horizontal rod. Behind the drain pipe under the sink is a horizontal rod connected to the lift rod via the strap. The horizontal rod is held in place by a nut. Remove the nut and pull the horizontal rod straight away from the pipe about an inch. The stopper should now come free of the drain.
There are two types of tub drain stoppers - lift & turn and toe tap.
Lift and Turn
The lift & turn stopper for the bathtub unscrews counterclockwise while in the full up position.
The toe tap stopper also unscrews counterclockwise while in the full up position. However, the cap may unscrew from the plunger assembly before the entire stopper comes out. In that case, there is a nut that will be exposed and can be used to unscrew the plunger assembly from the drain.
If either of these is "spinning" without unscrewing, the threads are stripped and you would need to exert upward pressure while unscrewing in hopes of uncoupling this from the bath waste. If that doesn't work you would have to unscrew the bath waste flange from the drain pipe.
This will require access under the tub.