Yes. There are three different types of sinkholes and their formation is dependent on the specific stratigraphy (the different layers of soils and rock below the surface) of a given region.
Cover Collapse Sinkholes
Cover-collapse sinkholes may develop abruptly (over a period of hours) and thus cause catastrophic damages. They occur where the covering sediments contain a significant amount of clay. Over time, surface drainage, erosion, and deposition of sinkhole into a shallower bowl-shaped depression.
Cover Subsidence Sinkholes
Cover-subsidence sinkholes tend to develop gradually where the covering sediments are permeable and contain sand. In areas where cover material is thicker or sediments contain more clay, cover-subsidence sinkholes are relatively uncommon and therefore may not be seen frequently. They are smaller and thus may go undetected for long periods.
Solution sinkholes occur in areas where limestone is exposed at land surface or also is covered by thin layers of soil and permeable sand. Dissolution of the limestone or dolomite is most intensive where the water first contacts the rock surface. Aggressive dissolution also occurs where flow is focused in preexisting openings in the rock, such as along joints, fractures, and bedding planes, and in the zone of water-table fluctuation where groundwater is in contact with the atmosphere. Solution sinkholes are generally small in size and also slow to develop.
You can read more about sinkholes on the USGS Website.