The charge carriers are particles, like electrons, protons, ions, etc. They can be of either type of charge, but in most common circuits they are electrons.
The unit of current is the Ampere. One ampere of current occurs when one Coulomb of charge passes through a material each second. Current is not determined by the speed of the charge carriers, but rather the number of them that pass through the material per second.
I = Q / T
Charge carriers, like electrons move at the same speed through insulators as they do through conductors. The difference between the two is that conductors will allow more charges to can get through than the insulator. This means that the total number of charges per second is greater even though they go the same speed.

The amount of current which passes through a material depends on the available spaces (referred to as holes) for the charge carriers in the material. Conductors have many holes for the electrons to fill while insulators have few holes. Electrons can only move into available holes. If no holes are available then the electrons can not progress; there is no current.
The textbook uses conventional current which is the direction of positive charge movement. Electron flow is opposite conventional current. The remainder of these notes will use electron flow.

Current comes in two forms; direct and alternating. In direct current the charge carriers move in one direction. In alternating current the charge carriers move back and forth in the material. Both of these can deliver energy to the load since the charges are moving. It doesn’t matter in which direction they are moving as long as they are moving.

If you consider a direct current it is important to note that a single electron does not travel very far in the material. It moves from atom to atom in a random pattern, but slowly drifts against the direction of the electric field created by the potential difference of the source.

This drift velocity is usually slow, but the effect is that the chain reaction of forces on adjacent electrons causes the an interaction which moves through the material at a speed close to that of light. This energy movement is the current. It is created by electron movement, but it is the energy movement which is important.
Consider the following analogy. Picture a pipe which contains four tennis balls. If a fifth ball is pushed into the pipe a ball emerges from the other end. Notice that the fifth ball moved a small distance, while the energy moved the length of the pipe in the same time.