why is aggregate demand equal to aggregate expenditure? AD is how much the people in market demand (or want to buy) goods and services. On the other hand, AE is actually how much they end up spending.

AD = AE = C+I+G+X-M

I can demand and not buy? wouldn't that make AE unequal to AD? so how can it be equal? 

Please, help. Thank you!
When we say that AD=AE we don’t mean that aggregate demand function is equal to aggregate expenditure - we mean by that the actual total quantity (Q) demanded on the market given the aggregate prices at a specific period of time is equal to aggregate expenditure. Aggregate expenditure is equal to the sum of all spending on output (Q) sold in the economy at the given time.

They must be equal because the total quantity demanded is actually quantity that’s being purchased on the market - it’s not some hypothetical demanded quantity that’s not purchased.