Yes, equipment is more like 'things; used in different technical circumstances - medical equipment [MRI scanning machine], gym equipment [weights]. Facilities are more connected to hospitality and buildings: toilet facilities, dining facilities, conference facilities.

I've always though of facilities as structural and equipment as stuff that can be moved around. Doesn't mean I'm right.

a place, amenity, or piece of equipment provided for a particular purpose. "cooking facilities" Similar: provision space means solution potential prerequisite equipment amenity resource service advantage convenience benefit establishment centre installation place depot station location premises site post base camp joint outfit set-up 2. a natural ability to do or learn something well and easily. "he had a facility for languages" Similar: aptitude talent gift flair bent skill knack A facility is the ability to do something and/or the equipment and/or place provided to do something. Equipment is just the tools or machinery to do something. Medical facility will have equipment and the place/space as well as staff doctors/trainers administrators etc. A university faculty will like wise be the same for studying learning and research An army facility will be the same but specialised for the army. Notice for university we use the word faculty, although you will often hear these words interchanged when speaking about a place where there is either staff or equipment or both.