Without looking it up, I was thinking that the telescope was the thing that looks out into space, and the observatory is the building it’s housed in.

The telesscope is the instrument gathering the radiation. The observatory is the everything at the location of the telescope dedicated toward achievement of that function of the instrument including the scope itself. Telescope is to observatory as 16 inch gun is to battleship.

Thank you @HP. You put it much more eloquently than I.

I have a telescope without an observatory. Think of an observatory as the house where the telescope is stored with all the stuff in there. All you need to do is take off the roof and boom, you’re ready to go (not really, but sort of).

In my case, I take my telescope and wheel it out of the garage to set it up. If I were to build a shack in my driveway and store my telescope in it with a roll off roof and everything then it would be an observatory. Of course that will never happen becuase my wife won’t let me.

I did think about building an observatory for my telescope in my backyard, but there were too many obstructions. I also often get data from telescopes that are in remote observatories.

Make sense now?

After reading the answers above, my thought is the Webb is an observatory because it hosts multiple instruments, and a quick trip to the NASA web site confirms.

https://jwst.nasa.gov/content/observatory/instruments/index.html

“Webb’s instruments are contained within the Integrated Science Instrument Module (ISIM) which is one of three major elements that comprise the James Webb Space Telescope Observatory flight system. The others are the Optical Telescope Element (OTE) and the Spacecraft Element (Spacecraft Bus and Sunshield).”

https://www.nasa.gov/mission_pages/webb/instruments/index.html

The ISIM includes the following instruments:
—Near-Infrared Camera, or NIRCam – provided by the University of Arizona
—Near-Infrared Spectrograph, or NIRSpec – provided by ESA, with components provided by NASA/GSFC.
—Mid-Infrared Instrument, or MIRI – provided by the European Consortium with the European Space Agency (ESA), and by the NASA Jet Propulsion Laboratory (JPL)
—Fine Guidance Sensor/Near InfraRed Imager and Slitless Spectrograph , or FGS/NIRISS- provided by the Canadian Space Agency

Without reading the answers above or looking it up, my guess would be that the telescope is the instrument and the observatory is the facility. Sometimes the facility is named for the instrument.