Flight and block hours
Don't get too concerned about not knowing the answer - you'll be surprised at how many aviation professionals stumble with this one!
'Flying experience' (referring to aircrew) is this total hours at the controls of an aircraft - on the ground and in the air - and yes, it includes start-up, taxi, flight and shut-down. This is usually referred to as 'flight time' and is the 'flight' component of 'flight and duty time limitations' which are used to prevent flight crew fatigue.
'Aircraft hours' (referring to entries in the aircraft log books) are the total hours from brakes-off on the runway for the take-off run to a full-stop (or almost full-stop) after landing while still on the runway. Run-up time and taxi time is not included. This is more often referred to as 'time in service' and is primarily used to schedule the required aircraft maintenance actions.
And yes, there are hard and fast rules about this, they can be found in airworthiness legislation (ANO, FAR's etc.) and vary slightly in definitions but the intent is the same.