Something bugged me about encirclements for a really long time. Outcomes and circumstances were so very different that different encirclements didn't seemt odeserve to be called alike.
Here's how I divide the generic "encirclement" into four distinct natures of encirclements
The prototype encirclement save for sieges. It greatly inspired von Schlieffen (who became obsessed about Cannae and encirclement) and was thus the inspiration for the German military theory focus on victory through annihilating encirclement.
Hannibal won in Cannae by holding the line (in part with delaying tactics, yielding some ground) in the centre and winning with cavalry on the flanks. The cavalry pursued the defeated hostile cavalry shortly, then proceeded to attack the enemy's rear. The smaller Carthagian army of mercenaries and South Italian rebels defeated the much larger and still intact Roman consular army. All Romans but those left behind in the fortified camp and some cavalrymen were lost.
The "cavalry on flanks" think became the norm again during the age of blackpowder.
The nature of this kind of encirclement is that the defender (encircled forces) are cut off from their logistical hub (camp), become dispirited, lack central command and control for a break-out through the overstretched attacker's perimeter and resupply during the battle is actually quite unimportant. The defeat is thus centrally about causing despair; the opponent is being broken morally.
(2) Blitzkrieg schematic
Enemy lines are being penetrated, some enemies are being encircled and cut off, and said cut-off force is very dependent on near-constant resupply with ammunitions for its combat power. Furthermore, the encircled force was typically inferior in movement speed and the encircling attackers often proceeded to push deeper into the largely undefended rear, thus widening the perimeter. Finally, the entire action is only successful if the encircled force is too weak to break out or even simply cut off the encircler's resupply lines.
The description of the encircled force in this kind of encirclement hints that we probably should not expect this to be relevant for modern mechanised force vs. mechanised force campaigns.
(3) Czechoslovakia '38 / Poland '39 (strategic level)
The kind-of "encircled" forces have their supply depots and even their industry and political centre with them.
The advantage of the encircling force is that this situation leads to a long front line which can only be defended with rather stretched forces and is thus difficult to defend.
There is also an advantage for the encircled force, though: It has the advantage of inner lines (a concept dating to Jomini IIRC), which means it can move its reserves more quickly from one fight to another.
Also, resupply is without special problems for both; that's a large difference to case (2).
(4) Disappointing encirclements
There are two such cases, one being abortive caste or city sieges and the other long-drawn, partially successful or ultimately failed encirclements in mobile warfare (Stalingrad, Demjansk, Falaise, moving pockets).
The characteristic of these encirclements is that the encircled force doesn't break quickly (especially not its morale) despite no or clearly insufficient resupply. Again resupply may be simple for the attacker.
The different natures of the beast aren't visible if one calls them all the same. Encirclement has greatly varying utility, depending on enemy troops and terrain mostly. A military thinker should be aware of the differences and not be lured into mixing them up only because there's but one or two (encirclement, siege) words for four different things.