So, the current through the diode is controlled by the voltage across the diode, and the relationship is exponential.

While all of this is completely true, I know from experience this is extremely confusing to beginners because this is all upside down from practical viewpoint; where diodes usually are used, known voltage is not deliberately applied over a diode, but the opposite is true: current which is defined by the other circuitry flows through the diode and causes an often unwanted drop i.e.

*loss* of voltage.

So you can turn the exponential equation upside down to get Vf on the left side of the equation: voltage drop seen over the diode is a logarithm of the current through the diode. And, logarithm being what it is, a pretty good bang-for-a-buck approximation over a limited range is a

*constant*, hence we see this advice that Vf of a diode is some 0.7V, depending on the diode type of course. In reality, it's not 0.7V but depends on current, but if current is within one order of magnitude from the diode rating, Vf doesn't change that much.

What comes to OP's question, I would try to simplify it this way:

Vf is a voltage drop or loss when the diode is conducting, for ideal diode this would be 0. This causes conduction loss P = Vf * I.

Vf is a per part number parameter; just simply look it up in the datasheet instead of confusing yourself with generalizations of gazillion of diode types and conditions. It's given in certain conditions like temperature and current. Like all parameters, it has variation between parts and hopefully manufacturer gives you

*minimum, typical and maximum* instead of just "typical" so you have guarantees to work with.

Lower Vf is most often desirable to reduce the power loss. But sometimes circuit designers take advantage of the diode's voltage drop when they need a specific (not highly accurate though) voltage drop somewhere in their circuit.

On the other hand, Vr is the voltage in the front page name (300V, 600V...) and it tells you how much the diode can take

*reverse* voltage when it's

*not* conducting. In this reverse direction, the diode drops all of the voltage available up to a limit where it blows up.