This type of restaurant is also described in the food biz as
adult fast food (1983) or as
upscale fast (1981). The term
fast-casual is much newer, dating only to 1995. In case you're wondering,
health-Mex (see the earliest citation) refers to Mexican cuisine that uses nutritious foods prepared in a healthy way, It's a widely used term that dates to 1993:
Not to put too fine a point on it, ZuZu does it right. That is to say, ZuZu serves food we love, despite the fact that it is clearly health-Mex, rather than Tex-Mex.
Lanette Causey, "ZuZu," The Dallas Morning News, August 12, 1993