A temporary repair works by adding something to the outside: a bandage, a sleeve, a patch of paste, a clamp over a split. It restores the surface but not the structure. That is fine for getting home and it is not fine for the next season of driving.
The distinction is not how long ago the repair was made but whether it carries load and seals by itself. A repair that depends on the failed part staying where it is has not fixed anything; it has only stopped the failure being visible.
Ask what the repair would do if the original material gave way entirely. If the answer is that the bandage would hold the section, the repair is structural. If the answer is that everything would separate, the repair is cosmetic and the original part is still doing the work.
On a TIG welded stainless section, that is the difference between a sleeve clamped over a split in a straight run, which is carrying very little, and a patch over a crack at a hanger, where the load is concentrated.
Exhaust gas finds paths that water does not, and a repair that stops the noise is not necessarily sealing. Paste and tape close a hole at the surface; they do not restore the joint face or the weld. A leak that has been quietened is still a leak, and it will erode the repair from behind.
Check for a leak properly after a temporary repair: look for soot tracking at the edges of the patch and for a change in sound when the system is loaded. Soot at the edge of a bandage is gas escaping past it.
A repair changes how heat leaves the part. A patch or a bandage insulates the metal underneath, so the base material runs hotter than it did and the difference in expansion between patch and pipe works the repair loose. That is why temporary repairs tend to fail at their edges first.
If the repair has been in place long enough to discolour, the material beneath has been through more heat cycles than the metal around it. That section now has a different history, and cutting it out of a stainless steel exhaust system has to account for that difference rather than assume the pipe around it is representative.
Watch for a repair that has started to move, a clamp that has lost tension, a patch that has lifted at one corner, or new soot at an edge that was clean. Any of these means the repair is on its way out.
A change in the sound of the car is also information: a new rasp or a whistle that was not there before usually means the repair has opened somewhere you cannot see from above.
Make it permanent when the repair has held through a full heat cycle and the part underneath is sound enough to weld, or when the repair has begun to move. Do not make it permanent if the base metal is thin, cracked around the repair, or has already been patched once.
Permanent means restoring the section: cutting out the damaged area, fitting sound material, welding it properly, then checking that the joint face is still flat. Anything less is another temporary repair with a longer expected life.