My wife used to work in an arboretum and did massive scale planting there and by herself in our greenhouse. The industry uses plastic plant ID tags of various styles including the solid spear and loop-back styles. Although those are rather thick and have no adhesive, there are literally thousands of plastic tags or labels available to this and other industries.
My wife has various machines called vinyl heat transfer machines which produce the plant ID tags. A roll of transfer tape (can be of various colors) is inserted along with a roll of vinyl transfer media. The vinyl transfer, as noted, can be thick like the spears or as thin as mylar. The later can have a really aggressive adhesive.
The machine I have in the shop is one of her spares and I've used it to print information on tubular shrink labels to put over wires for identification. Great for use on racecar wiring systems. In other words, these printers are extremely versatile. (pic 1).
The thin vinyl I have in there now is one of the smaller label styles. As I said earlier, these can be purchased in many sizes and thicknesses. The current software in the machine does text on two lines as entered on the keyboard (an optional extra) (pic2). You can also download graphics alone or in combination with keyboard entry. One could create the graphics for the engine tag on the computer and then download it to the machine as a graphic.
The thermal transfer does really solid colors as seen on the label I created here. Because it is done thermally, the transfer stays on the vinyl and is very hard to remove except by abrasion. The shininess of the label makes it appear as if it were laminated. Example in pic 3.
Just another rabbit hole to dive into as you require the machine, keyboard, software to drive the machine and thousands of different labels from which to choose.