Magnetic flux, Φ, is a scalar, measured in webers (or volt-seconds), and is a total amount measured across a surface (ie, you don't have flux at a point).
Magnetic flux density, B, is a vector, measured in webers per square metre (or teslas), and exists at each point.
The flux across a surface S is the integral of the magnetic flux density over that surface:
Φ = ∫∫SB.dS
(and is zero for a closed surface)
Magnetic flux density is what physicists more commonly call the magnetic field.
It is a density per area, rather than the usual density per volume.
(and they can't be used interchangeably)
Similarly, electric flux is a scalar, measured in volt-metres, and electric flux density (also a density per area), E, is a vector, measured in volts per metre (and is more commonly called the electric field).
Some sources say that magnetic flux density is not related to current but to VOLTAGE. I dont understand why. I always thought that the magnetic field in a wire is caused by the movement of charged elements (e.g electrons) in a wire. Can you explain this?