The terms don't seem to be used consistently. Most common usage I believe is that a converter converts electricity from one form to another to be used as a power source. For example a 120 volt AC to 12 volt DC converter converts AC outlet power to a constant 12 volt DC supply suitable for running lights, computers
, radios, etc. It is a poor battery charger because it puts out a constant voltage too low to efficiently or maybe even completely charge a battery.
Most battery chargers are poor converters. Some of the older styles require a battery in the circuit to operate correctly. Modern 3 stage chargers deliberately change the voltage over time to quickly charge a battery. Some (most?) modern chargers also say not to be used without a battery connected. Some have a setting to be used as a converter without a battery in the circuit.
Your link says a 3 stage converter is not a battery charger. I have never seen a 3 stage converter, it doesn't make sense in what I believe is common usage. There are poorly designed 3 stage chargers that don't charge the batteries as fast as they could, but there is no reason to have stages to supply power for use by devices.
There are also converters like DC converters, 12 V DC to 24 V DC, 24 to 12 , etc.