I have my tire fixed with a plug, but what I missed from the person who fixed it is whether this is just a temporary fix to get to the shop to put on a new tire or if the plug is good to the end of the tire's life?

If your tire is tubeless, and the hole was on the tread not the side wall, this is the correct way to fix the hole. Nothing more to do. I have over 20,000km on a tire with a plug in it

Ride, enjoy, repeat . . .

Tire plugs inserted from outside the tire aren't designed as a permanent fix. They're made to get you to a shop where you can have the tire repaired properly – with a patch plug inserted from the inside of the dismounted tire – or replaced, and no farther. At least that's what most tire manufacturers say. In the real world, if a plugged tire holds air many riders put off further action unless the plug is in a problematic spot, such as close to the side-wall, or in the case of a large or irregular hole that took more than one plug to fix.

Some of us have ridden thousands of kilometers on plugged tires with no problems. Whether you follow our dubious example depends on your tolerance for risk. While some plugs last the life of the tire, others are sawed in half by the flexing of the tread's underlying piles or come out because of improper installation. At the very least ride conservatively on a plugged tire, stay alert for the signs of deflation, and check the plugged location and air pressure often.