You may be asking about the UL recognized component mark, RU with a backward facing R. That mark is for components that will be part of a larger assembly which will will have its own UL listing. Using recognized components makes it easier to obtain UL listing for the entire product. Builders of custom-made equipment can be authorized by UL to apply the UL label to equipment that is constructed using only RU components. Authorized builders do not need to have UL individually review each item that they build. That is my summary of that program. Full and accurate information can only be obtained from UL.
I have been using contactors and relays for many years and have never encountered a description of "industrial" or "residential" or applications. Contactors and relays are primarily rated for current and voltage levels. They generally have different specified current and voltage ratings levels for AC and DC and for resistive and inductive loads. Manufacturers state what duty a device is designed for and obtain a listing that is appropriate. Some devices have a definite-purpose rating. What is covered by that would be detailed in rating sheets and other documentation. A device could be listed for a specific use, but that use would generally be defined by voltage, current, operating temperature and other such characteristics, not by named categories. However "tungsten lighting" and "motor control" are categories that may have defined requirements. These are things that would need to be discussed with an advisor assigned to your account with the testing laboratory.