Re the electrolysis method, it's not actually removing rust per se, but rather converting it back to proper iron (Fe).
Rust happens when iron (Fe) loses it's valence electrons, and you're left with a Fe ion and something else to make a salt. When you apply the anode and cathode the right way around, you'll have electrons propagating from the sacrificial metal to the object you're trying to "clean". Ie it's an additive process, if you will.
Compare this to the acid method, what you're doing here is actually removing the rust itself by solving it in acid. This is actually removing rust that could be converted to good metal with the electrolysis method.
Note, I'm not a chemist, the above is just what I remember from my chemistry a-level.
