Yes, many higher-end cameras offer image stabilization, but how it works depends on the brand.

For Canon and Nikon DSLRs, stabilization is generally not built into the camera body. Instead, it is provided in certain lenses, so only stabilized lenses give you that benefit.

Sony, Olympus, and Pentax commonly use in-body stabilization, where the camera sensor shifts to reduce shake. Sony calls this SteadyShot, so with those systems almost any attached lens can benefit from stabilization.

Panasonic was also mentioned as relying on lens-based stabilization in this context.

So the short answer is: professional and semi-professional cameras can have stabilization, but it may be in the lens rather than the body. "SteadyShot" is specifically Sony’s name for its stabilization system, not a universal term.