“One in the same” will generally be considered wrong. No dictionary recognizes it. You should avoid it and use the standard form of “one and the same.”
Chomp at the bit appears more often in most modern written sources than champ…;
Dictionaries make no comment about chomp’s correctness;
A small survey suggests that most people would edit chomp to champ;
I comment on it in my Fowler, but only one other usage guide does;
Insisting that champ is the only correct form seems to be a 'thing'.
The rule seems to be that if a candidate can recite half a dozen policy positions by rote and name some foreign nations and leaders, one shouldn't point out that he sure seems a few whereases shy of an executive order.
The above is a superlative example of the creative potential of the idiom frame ‘a few X short/shy of a Y’, e.g. ‘a few fries short of a Happy Meal’.
As a further historical footnote, it is interesting that the legalistic, ritual use of whereas as a preamble to legal documents led to its being used as a noun, defined as follows in the Urban Dictionary of its day, Grose’s 1796 Classical Dictionary of the Vulgar Tongue: