Both a mouse and trackpoint are directional tools. Neither one provides absolute positioning (as a touch screen or graphics tablet does). They’re both relative, in that they indicate the direction to move the pointer. The difference is that the amount of a mouse’s movement translates into an amount of pointer movement, while a trackpoint’s movement translates into the velocity of pointer movement.
I slightly disagree. Most OS's and mouse drivers allow you to choose the acceleration rate, including zero, and zero makes the mouse absolute. Likewise tablets can have nonzero acceleration rates. Even touchscreens can have acceleration - "flick" a scrollable screen and it will often continue to scroll after your finger has left the surface. Trackballs are another reasonable choice, which work like an upside down mouse with all of the same configuration options. Even a traditional joystick (with ratiometric output, not just bang-bangs) can work positionally, even absolute position.
The Big Loser is the eraserhead. It ONLY conveys direction, which abstracts the user an additional degree from what is almost always intended:
Position. It's not just less useful, it is
impossible to configure an eraserhead to operate in
any kind of positional mode. All of the other input devices can be dumbed down to act like an eraserhead (if desired), but an eraserhead cannot be configured to act like the others. It is a fundamental failure of the design.
I do respect those who really love their eraserheads. It's a small niche market group but they do exist and my hat is off to them, being able to achieve some measure of usefulness from such a fundamentally limited device.
EDIT: To be fair, there is a potentially improved eraserhead mode. It requires an eraserhead that senses pressure on its two axes. If you have that, theoretically you can translate that pressure to relative distance, yielding a positional offset from point of origin. Two limitations immediately become apparent. First, it requires a
remarkable degree of fine motor control in a single finger to achieve any sort of positional accuracy. Second and more crucially, what should happen when you release the eraserhead? Should the cursor snap back to its original location? Or should the driver assume you meant to leave the cursor wherever it was when you released? What defines "release", and should the driver accept or ignore (what it interprets as) small unintentional movements just prior to release? Or just anchor to the "greatest excursion"? If the latter, note you cannot reverse direction without an intermediate release of the eraserhead, to "reset" its idea of greatest excursion. These are not small problems, and we studied them back when I worked on Human Input Devices in the 80's. The eraserhead was the butt of many jokes for some valid reasons.