In macroeconomics I came across two type of crowding out. First, in IS LM model where in classical case, when LM curve is vertical increase in government expenditures have no increase in output i.e. full crowding out. Secondly, in AS AD model due to increase in government expenditures when AD curve shift in classical case i.e. Vertical AS curve there is no effect on output. What's the difference between these two cases of full crowding out.
A vertical LM curve means that any change in government expenditure will result in a change of the interest rate which exactly offsets the initial change of public demand (private demand increases/decreases).
A vertical AS curve indicates the level of long-run output. If AD shifts, all that this will create is a change in prices in the long-run. This is also called the Classical Dichotomy: real variables are independent of monetary variables.
So, both diagrams tell the same story about crowding out: changes of private expenditure offset changes of public expenditure. The diagrams just highlight different parts of the same mechanism.