How could you be moving in one frame of reference but not in another?

That happens all the time. The answer is: One frame of reference

is moving inside the other one.

Example:

- - You're sitting still, comfortable in a soft seat, reading a book.

In the frame of reference of the seat, you're not moving, and

neither is the book.

- - The soft seat is in Row-17 of the passenger jet you're flying

in, at 37,000 feet. In the frame of reference of somebody on

the ground, you're moving at 500 miles per hour.