Yeah, the strength of the tap and how often you use the crop will depend entirely on the horse and their mood and willingness. A crop tends to be used for a couple of light taps or for a harder 'pay attention to me' tap. You can use it on the shoulder without taking your hands off the reins, or behind your leg with one hand.
A dressage whip is more suited to a series of light taps as reinforcement. You shouldn't whack hard with it as it's much longer and thinner and therefore can hurt if you give a proper whack.
Sometimes you just need the crop in your hand to get a more forward horse. Sometimes you need to use it once or twice and then they move off your leg. Some days you end up having to reinforce every aid you give.