I've talked before about how I dislike RPGs that draw the focus to the system instead of to the fictional situation. It's the difference between deciding to use a hammer instead of a sword when fighting a giant crab because you think the shell would make stabbing difficult, vs. deciding which weapon to use based on to hit modifiers and damage potential.
There's been a forum discussion over the last few days (started by a troll, but now expanding well beyond the troll's intention) over the merits of grid-based combat compared to gridless combat or abstract combat. Although some would argue that being able to see the positions of the characters and monsters should support "fiction first" more than "system first" play, that's slightly inaccurate, since "grid-based combat" implies a lot more besides simply using minis and terrain models. It implies at the very least that there are facing penalties and movement costs, and possibly much more.
I think a lot of these discussions run into a problem because many players who only like grid-based combat think that the opposite method would be to use those facing penalties, movement costs, and other rules keyed to exploiting the grid, even though no grid is present. Thus "gridless combat" would have all the rules, but not as much visual appeal, and at worst, it may be difficult or impossible to run without a grid. This covers the two kinds of comments I've seen about grid vs. gridless combat.
In contrast, abstract combat would not just be gridless, but wouldn't have many of the rules associated with grid-based combat. For example, some systems have a movement cost to change facing, while others specify to what degree you can change facing in one round. In abstract combat, it is assumed that, if an attacker failed an attack roll, it may be because you turned to face him.