It can sometimes vary by manufacturer in its exact name.
It used to be called "motor drive" mode because in film cameras, usually an external motor had to be added.
On Canon cameras it's called "continuous drive mode". Basically every DSLR out there supports this feature. I don't know of any that do not have it. The difference is going to be in terms of how fast and for how long a burst can be sustained. (Burst is another term you'll see, typically in specifications of how many frames per second for how long.)
Some cameras give you a choice of a high burst rate without autofocus between shots and a slower rate with autofocus between shots.
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