Hi Dale,
First of all, magnetism IS a hard subject to understand, so don't feel that you're an exception in finding it tricky. It took me a long while to grasp the basics and even now I only know as much as I need to.
Next, to your question. The easy part to understand, as you point out, is magnetic flux density. It is analogous to the pressure in a tube with water flowing inside it. This pressure is force per unit area where the area is that of a vertical slice across the tube. Replace the tube with a solid magnet and replace force by magnetic flux. Again imagine cutting a vertical slice across the magnet. With respect to the area of this slice,
flux density is the amount of magnetic flux per unit area, passing through the magnet.
Now we leave magnets altogether and instead consider wires through which electric currents are passing. As you know, such wires have a circular magnetic field around them (whose field directions are given by the right hand grip rule
https://www.gcse.com/energy/em4.htm ). Magnetic
field strength concerns the relationship between the the amount of current passing through the wire and the strength (ie amount) of the resultant circular magnetic field. Note the clear difference: Mag. flux density concerns
magnets whereas mag field strength concerns
current bearing wires.
If however, such a wire is bent into a loop, a linear (as opposed to a circular) magnetic field is generated through the loop, ie field direction is perpendicular to the plane of the loop. And if instead of a single loop, the wire is bent into a coil of several loops (such a coil's formal name is a solenoid), the linear magnetic field is proportionately strengthened. This linear magnetic field is the exact replica of the magnetic field through a magnet. It is as if an imaginary magnet exists inside the solenoid. Incidentally, the relationship between the linear magnetic field and the current in the loop is given by Ampere's law (discussed further here: **broken link removed** ). And since we are back with magnets, albeit imaginary ones, we can apply our concept of mag flux density to such a magnet. This is the inter-relationship between mag flux density and mag field strength.
To summarise: mag flux density relates to magnets; mag field strength relates to current carrying wires; bending such wires into loops produces 'magnets', and by this method we can relate mag field strength with mag flux density.