There are many sports of theatre spot - mostly tungsten filament, but with different lenses to give different beam patterns and different spreads of light. Some have facilities to slide a coloured gel in, or to add barn doors.
otherwise there isn't much difference between a tungsten theatre lamp. A lamps a lamp.
One difference is that a theatre lamp is normally designed to hang below a bar, and some bulbs have markings to say which way up they're designed to work - using them the wrong way shortens bulb life as sometimes the hot and fragile filment isn't supported by various things in the bulb over its whole length.
I've used my drama groups lamps for photography - no problems.