Gravity seems to act like a force, but has been shown to not be like the other forces. It's different.
How? Why?
Prerequisite knowledge: Both momentum (mass times velocity) and kinetic energy (half mass times velocity squared) are conserved properties.
Forces act with energy. They use energy to change things. Two balls hitting each other exchange kinetic energy, thus altering their momentum.
Gravity directly affects a ball's momentum, thus altering its kinetic energy. Gravity doesn't use energy to achieve its effects.
It's that simple.
Not quite so simple: There are both objective and subjective time and, thus, velocity. Objective time ticks along, moving things a certain distance in a certain time. This is objective momentum, and is how photons move and change over time. Subjective time ticks along faster or slower, stretching or shrinking perceived space along with itself. This is subjective momentum (kinetic energy), and is how matter moves. Photons don't have subjective time.
If momentum and kinetic energy are conserved, where do they come from when gravity accelerates something? Space-time itself. Space-time is a field of potential energy, from which all other fields and effects withdraw their energy. In other words, kinetic energy + potential energy = constant, at every point.
Space-time is the field which governs motion, involving both time and distance.