Electrons are supplied by the voltage right?
No, electrons are "supplied" by the conductor (in the case of typical metal conductors). In fact they are naturally present. Note that in other types of conductor the charge carriers may be something other than electrons.
The voltage just "supplies" a force that pushes those charge carriers slowly along.
The source of the voltage, for example a battery, does supply charge carriers, but it is the battery supplying the carriers, it is not the voltage supplying the carriers.
The drift velocity in metals (and hence current in coulombs of charge per second) depends on electron mobility and electric field (which is measured in volts per metre)
Conductivity is proportional to the product of mobility and carrier concentration. Conductivity is a property of a material, it's inverse is resistivity which is measured in ohm metres. For a given length and cross-sectional area of a material you can calculate resistance in Ohms from resistivity of the material.
So a lower resistance (higher conductance) implies higher mobility (carriers can move faster) or higher carrier concentration (more carriers) - either lead to more current.
Isn't current the number of electrons flowing?
Not exactly. It's the number of electrons (or other charge carriers) flowing past a specific point per second. It's a rate not a number.
Maybe an analogy will help: Think of cars travelling along a highway as you stand on a bridge watching. The number of cars passing per minute does depend on the number of cars per mile of highway (the carrier concentration) but it also depends on the speed of the cars (related to carrier mobility).
Say you have a uniform density of cars along a 120 mile circular highway like the M25 around London. You are standing on a bridge counting cars passing each minute. If all those cars are travelling at 30 MPH (because the speed-limit signs have been set to 30) maybe you measure 10 cars passing a minute. If the cars are later all travelling at 60 MPH, you would measure 20 cars per minute without any change in the number of cars on the highway and no change in their density (concentration).
The speed of the cars depends on the propelling force (like voltage) but also depends on rolling resistance, air resistance, the need to negotiate junctions and around obstacles etc. Of course charge-carriers don't have built in engines for propulsion, maybe they are more like wind-driven or solar-powered batteryless vehicles.
Like all analogies, you don't get far before it becomes misleading. At the atomic level, the charge carriers are all in perpetual random motion but don't move far on average unless there is an additional force provided by an electric field (measured in volts per metre) that causes them to, on average, drift in a specific direction. Their movement is impeded by the characteristics of the material, this is a resistance to their movement.
Note that charge carriers in motion are carrying energy from one place to another, this is somewhat more important than the carrying of charge because the net movement† of charge is zero (in the car analogy, there are always as many cars in sight in each direction from the bridge no matter how many cars are in motion or how fast they move)
†What I mean here is that after a period of time, there are still the same number of charge carriers in a portion of conductor as there were at the start. There has been movement of carriers around the circuit - so there is charge movement - but the net effect (on number of carriers, and charge, in the portion of conductor) is as if there had been none. On the other hand, energy is dissipated in the conductor due to this motion, so you can tell from the elevated temperature of the portion of conductor that there has been motion of charge carriers.