Did you ever wonder how a word came to be? I do, all the time, so I looked up these two words. According to Dictionary.com, cheapskate comes from " 'miserly person,' 1896, from cheap (q.v.), second element perhaps from Amer.Eng. slang skate 'worn-out horse' (1894), of uncertain origin."
Worn out horse? Well... ok. What about tightwad?
Again, quoting Dictionary.com"'parsimonious person,; 1900, from tight in the sense of 'close-fisted' (1805) + wad. The notions of stringency and avarice also combine in Mod.Gk. sphiktos 'greedy,' lit. 'tight.'"
Greed? Stingency? Avarice?
I like the word "frugal" better, but all these are all used to mean the same thing, at least in certain circles. Let me put it this way: Sometimes I can be a definite tightwad in the sense of close-fisted. The rest doesn't apply. I'm not sure about the cheapskate.
Are you miserly? Do you grasp and hoard and try, even with a little avarice, to "get things"? I didn't think so.
Frugal, I am and I'm not ashamed to admit that. The rest... well, I'll leave that to others.
frugal: "1598, from M.Fr. frugal, from L. frugalis, from undeclined adj. frugi 'economical, useful, proper,' originally dat. of frux (pl. fruges) 'fruit, profit, value,' related to fructus (see fruit). Sense evolved in L. from 'useful' to 'profitable' to 'economical.'"
(Also from Dictionary.com. I'll let you look it up yourself.)