I think that for all intents and purposes, Warwick's Discrete Maths course is just their name for computer science and maths joint honours. The only difference may be that the computer science and maths elements are more tightly integrated than at other universities. I've certainly applied under the assumption that it is more or less the same as a CS and maths joint honours.
I think that applying for Discrete Maths at Warwick and straight CS elsewhere would be a bit odd, since approximately half the Discrete Maths course is maths (as far as I know). The reverse, applying to mostly joint honours courses and one straight CS one (e.g. at Imperial where JMC is allegedly super maths intensive) is more understandable. You don't need to worry about how it will look - universities don't see who else you've applied to, and you can easily write your personal statement to cover both. But you do need to decide which way your interests lie.