I'm not an EM guy, but you might find it easier to understand
the words in for something like heat flow. "Flux" is the total
amount of heat flowing through a surface (measured as heat
energy / second, i.e. power in watts) "Flux density" is the flux
per unit area, or sometimes the amount of heat generated per
unit volume (for example heating something in a microwave oven,
or heat generated by nuclear reactions). FWIW, temperature is a
scalar field (which is simpler to visualize than the vector
fields in EM) and the direction of the flux is therefore the
gradient of the temperature field. If you visualize a
temperature distribution on a plane by drawing a contour map,
the flux direction is at right angles to the temperature contour
lines, and the magnitude of the flux density is higher where the
temperature contours are closer together.