I'm trying to research various types of movement rules in tabletop games, to in turn make homebrew improvements on other games.

These are the systems I'm familiar with:

Storyteller: In it's various incarnations, the ST system uses a "Distance Per Interval model", but does not employ any form of map or absolute positioning mechanic. It's usually Yards Per Action or Yards Per Second, depending on your interpretation. Tihs is a facing-agnostic system, compared to DnD.

Dark Heresy: Movement is defined by deliberate action, and those actions give you increasing distances traveled. Free Actions let you move a little, Half Acitons let you move further, and Full Actions let you move the furthest. Dark Heresy also assumes maps will be employed, but not in a strict, grid-model.

Dungeons and Dragons 4e: Grid based, with movement being defined as how far you can move or how far you can force someone else to move. This system includes facing rules and other related mechanics.

FATE: Fate uses Zones, which are vaugely defined volumes of space in a given environment, which in turn are composed of elements that can be invoked. Your absolute and position in the zone is flexible, as the game cares more about you being In the same zone as whoever you're interacting with, than it does with where you are in the zone.

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Any input on this matter would be greatly appreciated!

Another source you might want to look at is GURPS. Fourth edition is most recent, but movement rules didn't change too much from third edition. It's a hex based system with one yard per hex. Movement is generally given is hexes per second and there are facing rules. GURPS has a large array of optional rules including things like turning radii for high speed movement, tables for exact accuracy penalties based on speed of target and so on.

I admit I'd rule Hex-movement under Grid Movement, as a subtype of Absolute Positioning.