I think that 1 and 3 are both specific types of 2, as both are defined to be adiabatic - which just means thermally isolated.
Type 1 is when a thermally-isolated container is divided into two parts separated by an openable divider, with one part containing gas and the other a vacuum, and the divider is then opened, to allow the gas to expand into the vacuum part.
Type 3 is a more complicated process (explained
here) where a gas is forced through a valve or porous plug, and the system where this happens is thermally isolated.
Both 1 and 3 are irreversible processes.
An example of an adiabatic expansion that is neither type 1 or 2 would be where the gas in a cylinder expands by pushing back a piston, while remaining thermally isolated. I think (but am not sure) that that would be a reversible process.