Band Gap type sensor usually use the materials from the periodical table elements of IVa like Si/Ge/Sn/Pb to form semiconductor with elements from VIa like S/Se/Te; sometimes you could use VIII element such as Zn/Cd/Hg. More often you see III-V like In/Ga-As/Sb. These are considered semi-conductive materials. Although some of these materials could have other characteristics such as those mentioned below.
Micro-structure is like using micro-machining to make (most of time) Wheatstone bridge type circuit in a micro scale. Of course, band gap type device could be made in the form of a micro-structure. But in our case, we are trying to separate the sensors from their base materials. The sensitive materials in a micro-structure type IR sensor usually are PZT, PVDF, etc. They are usually pyroelectric and ferroelectric materials. Although some of the materials could be semi-conductive or even piezo-electric materials but people are using them based upon their pyroelectric and ferroelectric characteristics.
I searched some sites to give you more background. it is all depends on listener’s background, and how much they want to understand. Even Mike and I could give different definitions. In some of the cases, it is marketing that determine the name. Like Honeywell micro-structure mass flow sensor, the basic theory is the same as thermal mass flow sensor. But it sounds hi-tech calling "micro-structure".