Irreversible process (Isothermal and Adiabatic) How exactly would we define an irreversible change for an isothermal process? Why can we say what the external pressure will remain constant? Please give an example.

Also, why can we not define both reversible and irreversible processes for adiabatic process simultaneously?
$$\Delta E_\mathrm{rev} = \Delta W_\mathrm{rev}$$
$$\Delta E_\mathrm{irrev} = \Delta W_\mathrm{irrev}$$
I got that if these both take me to the same point then $\Delta E$ will be same, but why must $W_\mathrm{rev}$ and $W_\mathrm{irrev}$ be different?
If you have an adiabatic reversible path that takes you from state 1 to state 2, any irreversible path from state 1 to state 2 will require removal of heat, so it won't be adiabatic.  This is a consequence of the 2nd law of thermodynamics, captured by the Clausius Inequality.