Depending on the environment that you are developing in you could use either; however, searching stepper in regards to UX design returns more results leaning towards Google's definitions.
UX Planet uses stepper in the context of a stepped process, for example account registration or order delivery.
Guiding users through a complex process by making it easy and intuitive is key to helping increase conversion rates. Any frustration along the way may cause them to leave and pursue other options.
An easy-to-use stepped process helps users avoid frustration and successfully complete a primary task. In this article we will overview various uses of progress trackers and see how they can be implemented.
Wheras the iOS documentation seems to use a stepper in regards to a numerical selector, for example item quantity.
A stepper is a two-segment control used to increase or decrease an incremental value. By default, one segment of a stepper displays a plus symbol and the other displays a minus symbol. These symbols can be replaced with custom images, if desired.
Neither are more "right" than the other, however using stepper to describe incrementing a value in a non-iOS oriented environment might cause confusion.