The Op question was glue vs no glue. I can only assume that the no-glue gum has encapsulated solvent that gets ruptured during the act of shoving it into the hole.
I have used about all of the plug types over the years with very good results. Good enough that I consider the tire fixed. I have had a few failures due to the hole too close the edge or too big for a plug but that still leaves me with a 95% success rate and I always have the option of getting it patched, later.
My thoughts and experiences are as follows:
Fix-a-Flat - Good for wives or girlfriend on side of the road. This is a can of air injected thin sealant that will also partially inflate the tire. The tire HAS to be spun to get the sealer to the leak and the sealer is going to be flung to the furthest from the hub as possible. Tire may have a flat tread but the inside is round and there has to be enough sealant to wash up the curve to reach the hole. I don't care for it and don't trust it. If it doesn't work right away where you can drive the car and spread the goop around you are going to have a blob of snot throwing off the balance. Many shops won't even fix tires with Can O' Snot in them. I always cringe when folks dump in cans of this stuff to try sealing rim leaks.
Slime - tried it once on garden tractor tires. Didn't have much luck. It oozed and didn't start harding until it was on the driveway.
Plug Kits: Lots of choices and my reasons to use what I do.
1. Glue or no glue. Both work but I lean to glue for the previously posted reason of lubrication and getting sealer into the edges of a tear. Give the glue some time to set up and work its magic.
2. Reamer - Sharp rasp/file style or smooth twisted edge style. While the rasp will roughen and clean the hole better, it will also tear up the belts. The smother type will push the cords aside and I think that helps retain strength and shape in that area.
3. Insertion tool - Open at the tip type. Thread the plug and push it in. The plug escapes the tool through the slot as you pull out the tool. If you have short plugs or push too far you can lose the plug in the tire. There is a side slot type that will allow push and twist to release or push and pull to double up the plug. While a neat idea, most I have seen are cheaply made with soft metal and the nose breaks off. The closed loop style, which looks like the end of a large sewing needle has no slots and even if cheaply made will be stronger and give full control over the plug.
Plug types:
Thick, thin, black, red and tan snot covered ropes or soldid rubber plugs. Some may be labeled for Bias or Steel belted radial. Those labeled for steel belts are usually thinner and denser as to tear less when pushed through past ragged steel wire ends. I prefer the denser cords and a closed push/pull tool so I get 4 strands in the hole for the extra density and they can slide around and fill jagged holes better. Not every hole will be made by a nail.
So, for a complete kit you want...
A pack of long thin dense cords. I can double up with push/pull or add another plug. (Trying to force a fat plug in a small hole breaks tools or you have to make the hole even bigger)
A can of glue. (Yes, it costs more but you just can't dip a reamer or plug loaded tool otherwise and trying to dribble and smear a limited supply of glue on the freeway in bad weather is just not worth the hassle.) Keep a tube in case your can dried up.
A closed type tool, preferably a quality smooth and tempered unit.
A smooth twisted reamer / locater.
A pair of flush cutters or razor knife.
A pair of pliers and a screwdriver to dig out the troublemaker.
A few cans of air or a pump.
This assumes a roadside repair:
Find the hole and move the vehicle so that the hole is easier to work with. A front tire at 7 to 8 O'clock or a rear at 3 to 4 O'clock seems best. You want room to push and pull without fenders around to whack your hand on if something let's go.
Break out your flat fighting kit and get the can of glue open and put the reamer in the glue. If you need to retain the air in the tire as much as a possible this part can get messy.
Use pliers and screwdriver to remove the nail, screw or piece of ornamental railing from elaborate mailbox you just ran over. In fact, slowly drive to another street so you are not easily connected to the crime and start over. As soon as the nail or screw is free grab the gluey reamer and guide it into the hole and ream a few times to spread the glue and displace moisture if it has been raining. This is the messy bit if there is enough air pressure left to blow glue around as you are probing with the reamer or inserting the plug.
Leaving the reamer in the tire get out a plug and the insertion tool. If the reamer seemed tight and the hole small, you can cut the plug in half if 4 cords seems too much. Thread the plug into the tool and dip into the glue. With a full length plug threaded on the tool the tail ends of the plug should reach beyond the tool shaft and past where the handle begins. You don't need glue that far up as it will spread up when pushed into the hole.
Remove the reamer and push in the plug. If using a half plug you will push until the plug is all inside the tire then pull out until the tool tip is just above the tread and you can cut the plug off the tool. This is a 2 cord plug. With a full length plug you push in until the plug tail ends are just above the tread and then pull tool out, doubling the plug (4 cord) until the tool tips allows cutting off the plug.
By using the push/pull method you ball the up the glue and softened plug goo on the inside of the tire, during the pull, where air pressure will force it back into the hole for a better seal. A push only plug will ball it in the tread leaving dry gaps on the inside.
Leave it all to sit a bit while you clean off the reamer, close the glue, adjust fake nose and glasses in the case of the mailbox while the glue does its thing. Trim the plug flush with the tire ALWAYS. While you can drive off as soon as adding air you don't want to stress the bond while the chemical reactions are still taking place by driving over a big knot of plug pushing it in.
As far as my experience goes, around a hundred roadside plugs for simple nail and screw holes, this is a done deal. If the hole was big or is cut from glass then I would get a proper patch ASAP or replace the tire.
I will use a properly plugged tire over an emergency donut any day. Donuts are usually way too small in size and load rating, causing steering a handling issues, and have speed and distance limitations that make them a last resort in my eyes.
Anyhow, I see that I have gotten log winded, again, so please accept my apologies. I am running a fever and had just better crawl back into bed.
Nite nite