reversible expansion vs. irreversible free expansion

[Daniela Shatzki 2E]

Could someone explain the difference between isothermal, reversible expansion and isothermal, irreversible free expansion? They are mentioned in question 4I.9 on the homework and I'm not really sure what they mean.
"Initially an ideal gas at 323 K occupies 1.67 L at 4.95 atm. The gas is allowed to expand to 7.33 L by two pathways: (a) isothermal, reversible expansion; (b) isothermal, irreversible free expansion. Calculate ΔS tot, ΔS, and ΔS surr for each pathway."
I figured out the answer to the question but I don't really understand the difference between the two pathways.

[AArmellini_1I]

The only real difference is how the work was done. In an irreversible reaction the expansion occurs instantaneously, where as in a reversible reaction the expansion occurs over infinitely small expansions.

[JasonLiu_2J]

In an isothermal reversible expansion, the system does work on the surroundings when it expands, whereas no work is done on the surroundings in a free expansion. As such, w=0 in a free expansion and the deltaS of the surroundings will also equal zero. However, since deltaS is a state function, the deltaS system in the free expansion will be the same as that of the isothermal reversible expansion, since the system still reaches the same state following the expansion.