Enclaves are generally also exclaves, though exceptions exist (as detailed at list of enclaves and exclaves), and in common speech only the term enclave is used.
An enclave is an area surrounded by another area, while an exclave is an area cut off from the main area. An area can be cut off without being surrounded (such as Kaliningrad Oblast, cut off from the rest of Russia by Lithuania, Poland, and the Baltic Sea) hence exclaved without being enclaved, or surrounded without being cut off (such as the Kingdom of Lesotho, enclaved in South Africa, but not exclaved).
A pene-enclave (resp., pene-exclave) is an area that is an enclave "for practical purposes", but does not meet the strict definition. This is a very technical term.
(third-person singular simple present enclaves, present participle enclaving, simple past and past participle enclaved)
- To enclose within a foreign territory.
From French enclave, from Middle French enclave (“enclave”), deverbal of Middle French enclaver (“to inclose”), from Old French enclaver (“to inclose, lock in”), from Vulgar Latin *inclāvāre (“to lock in”), from in + clavis (“key”) or clavus (“nail, bolt”). Compare inlock.