A lot of the differences people ask for within the boundaries of character work, illustration, and so on come down to things that on a foundation level don't have really that much significance. Style is usually a big one, but the deal with style is it's just the final icing on the cake. Strong foundations mean you can look at what defines a style and put it on top of the foundation and you're usually good to go. Having the analytical mindset to pick apart the tics of a given style is pretty much what defines the ability to do it, I think.
Subject matter can be another. Drawing inanimate objects, like cars and the like aren't something I enjoy drawing so I don't have any of them in my portfolio. I know (and have confidence now) that by applying the same principles I've learned doing figures that I can handle drawing cars just fine to the same degree. Granted, I tend to look for work that isn't object-heavy over person/character or story heavy anyway, so that particular one doesn't come up too much, but the style one does.
Convincing the client that just because you don't have that many examples of a particular style in your portfolio doesn't mean you can't do the style they want, is a hard sell sometimes because they seem to be of the impression that an artist's style defines his or her limitations. Then there's people asking for Anime-Manga style when I just can't bring myself to deal with because I have a fairly strong dislike for the asesthetic. (If they offered huge$$, I might change my opinion of the style, but that's a financial consideration
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And on the artists' side there's the fear that you mention, but it's all the same foundation. If the foundation is strong, it can support just about all the variety you can imagine. Going more abstract here, organic over there. Shape driven here, or texture driven over there (like Frazetta's drawings, loaded with interior surface marks that do the heavy lifting in defining form), the door is wide open for anyone who wants to walk through it.
But I hear ya. Some days you have the imagination mojo working, others you don't. What's great about actually finding work for clients is that a good client will have a pretty clear idea of what they're after, relieving you of some of the pressure to find the boundaries of your project on your own.