There is no difference, it's just semantics. We talk about body wash or body cleanser as well.
I cannot be certain it's that, but i own Chizu Saeki's book on skincare and she says japanese women love to wash their face, first with an oil based cleanser to remove all the makeup, and then another cleanser to remove the excess oil left. That may be the reason why you were told to use both these products.
I see no problem using these two cleansers, i suppose considering they're from the same brand, and from a reputable brand, they are not too harsh for your skin but after reading about that Seikisho cool cleansing gel, if it's washing your face and removing even the heaviest makeup as it's described, i would stick to this one, and sometimes switch for the other. As for the excess oil that might stay on your face after removing the cleanser, assuming it's not some sort of foaming product, i simply wet a cotton pad with floral water (i favor chamomile for its soothing properties) and wipe it off gently.
Also i don't know where you live (i live in Europ), but speaking only on the financial aspect, japanese skincare products are only available to me through internet, and my favorite site doesn't always restock once everything is sold. On top of that, i have shipping&handling fees to pay, enough to make me consider sticking to european brands. So using two face cleansers at the same time would be too expensive for me.
