If current increases in an coil, what exactly happens?

Hello!

I understand that when current is increased throughout a coil, the magnetic field (B) increases it's strength. I try to compare this with a permanent magnet. The magnetic field in a magnet is due to the electron spins and the force is due to them, when you increase the size of the magnet there is more mass = more spins = stronger field a more force.

But what about in a coil? more current means more charges = stronger field and forces?

I want an explanation as why does the force increase as well.
If there is a coil in a system, motor,holding unit, etc... We know by increasing current the force is increased greatly.