Although I have ticked your second option, either option could be valid ... it would most likely depend upon the CMMS (database system) being used.
Some systems open a Job for each and every PM when due; so, in such cases, the Job will already be open. At some places I have seen (and/or worked at) the biomeds would close that PM Job, then open another Job (probably later on) when (or sometimes if) parts become available. This has the added benefit of showing fewer "open Jobs" on reports to management or supervisors.
Personally, I always liked to leave any Job open until the equipment was finally returned to service. I used to consider that a more honest approach: that is, one that high-lighted the defects (which were often many) in the "system" ... generally problems in procuring parts and/or other shortcomings of resources. I might add that "management" were not always happy about what usually became quite a long list of "Job open - awaiting parts" lines on the regular reports. Some items remained like that for months (even over a year in one or two cases). Some times a decision had to be taken to scrap the item and purchase a new replacement.
The key issue here is that of the parts required. As you mention, the system may already allow to have specific parts available for the PM procedure. But if the PM "fails" and more parts are needed to effect a repair then a Job record shall be needed sooner or later. Then, as you say, the PM itself can be re-scheduled once the equipment is fully restored.
The secondary point (also as you mention) is that of recording details of faults etc. and action taken. Again, where such notes are made shall depend upon the CMMS being used. Some (older) systems allowed faults, actions etc. to be codified (very useful when analyzing historic data; especially of large data sets).
