Removable, permanent & high-tack adhesives all refer to how strong the glue on the back of your stickers are.
We can also call them; low, medium and high strength adhesives.
A popular measure of strength is 'peel adhesion' (read more here). Typical values for each category of adhesive are:
Removable adhesive = less than 19 N/25mm
Permanent adhesive = 20-28 N/25mm
High-tack adhesive = 29 N/25mm and up
The most popular adhesive used on stickers & labels is an acrylic, solvent-based, pressure-sensitive adhesive.
Pressure-sensitive means they stick more when more pressure is applied. Simple.
Manufacturers of self-adhesive label materials will vary the strength of the glue in 2 ways:
The tackiness of their adhesive
The thickness of the adhesive
To increase the tackiness, manufacturers use a slightly different adhesive formulation that will stick more. This is fairly obvious.
However, the 2nd way manufacturers vary the strength is through-thickness.; this sounds counter-intuitive, but it works.
Most adhesive coatings on the back of labels are ~20 GSM; this can increase to over 40 GSM for heavy-duty applications. Especially where the surface being stuck too is uneven.
If only 40% of the glue is touching the surface the label is applied too, adding more glue to fill the gaps can work brilliantly.
Here's some further reading if you want to learn more about adhesives used for labels & stickers: