In brief
Similar names of assistants can describe different actions. The important question is whether the system warns, corrects, or manages a particular function.
Useful to know
In assistance systems, a warning does not mean automatic intervention. NHTSA distinguishes lane departure warning, lane return assistance, and constant centering support. These are different behaviors, not just different marketing names. [1]
Adaptive cruise control, in turn, adjusts speed to maintain a set distance from the vehicle in front. [1] Its presence does not prove by itself that the vehicle also controls the steering wheel.
Practically when reading equipment write the verb: warns, corrects, supports. Then check the operating conditions in the manual. In this way, you are comparing a function instead of comparing only abbreviations.
Don't automatically translate "assistant" as self-driving. The auxiliary functions described require attention and responsibility from the driver. The material explains categories and is not a confirmation of the capabilities of a particular car without checking its equipment.
Sources
For further detail and to check the information: