The main difference from the merchants' point of view is that when they do an offer with Groupon they receive half of the proceeds from the 'coupon', whereas in for a 'discount book' they receive nothing. The Groupon offer is thus better viewed as a heavily discounted gift certificate. Otherwise there is little difference other than the scale.
As to whether you are too cheap to buy a coupon? Unlikely. More likely you are insufficiently cheap for the idea to hold appeal, as you are OK with buying the product you want when you want it, rather than jumping through all sorts of hoops and advance planning to save a few dollars. You are welcome and possibly correct to view this as 'wise'.
Advertising has always been misleading and disrespectful, at least going back to the Romans. I had never heard about Groupon until today, and find it mildly interesting, but the problem with it is that I have to pony up cash in advance for something sigh unseen (usually a service or a meal!) and I guess I am too cheap for that.
Rddle me this: how is Groupon different from one of those coupon books the local school kids sell?