Errmm... not exactly.
CV = Fleet carrier. Carries 2 CAGs. Various mods have increases to 3 or even 4 with late tech's.
CVL = Light fleet carrier. These were usually converts-during-construction from other ship classes like light cruisers or civilian liners but not always. Sometimes they were small simply because that's all the remaining displacement allowed to treaty signatories would allow. They are characterised by having a significantly reduced wing but are fast enough to operate with the big CVs. This class is not actually represented in vanilla HoI 3.
CVE = Combustible, Vulnerable, Expendable. Carries 1 CAG and is mis-named as CVL in HoI 3. Contrary to popular belief, the vast majority of escort carriers were purpose built and not converted from merchant hulls. They are characterised by being small, slow, pitifully armed and totally unarmoured. Typically operating older &/or obsolete aircraft due to their short flight decks. More suited to the support of landings & troops pushing inland, sub-hunting and ferrying aircraft as they simply can't keep-up with fleet carriers.
Not to say that they're cheap so you don't mind having to replace a few while the loss of a fleet carrier is a disaster.
Close enough, that I won't argue with it that much. Technically:
CV = Aviation Cruiser (CA was already taken by Armored Cruiser (which became heavy cruiser), so CV was used instead).
CVL = Light Aviation Cruiser (Smaller Air Group, same speed as the CVs)
CVE = Escort Aviation Cruiser (also called a Jeep Carrier, same speed as the convoys they were designed to operate with.)
The US and Japanese both used unarmored flight decks (even on the BC conversions) which increased carrier vulnerability but allowed for greater flexibility in hangar designs. This typically allowed the USN to use larger (and more varied/modern) air groups, and actually limited the types of aircraft that could be provided to the RN via lend lease for use on the Illustrious and Implacable classes.
So the RN used CV with the flight deck as the armor deck, with slightly smaller and limited flight groups but greater durability while the USN (and Japanese) used a CV with a hanger deck as the armor deck, but with larger and more varied flight groups but lower short term durability.
Technically the only difference between a CVL and a CVE was the speed. CVLs were designed to operate with the Fleet (particularly the fleet carriers) and so had similar speed to the CVs while CVEs were designed to operate with merchant fleets (either as escorts or to ferry aircraft to fleet units to replace losses). Most of the early-war USN CVLs and CVEs were conversions*. The CVLs were conversions of Cleveland and Brooklyn class CLs and the CVEs were conversions of oilers, transports, or civilian merchant ships.
*The vast majority of these conversions were converted during construction and not after their launch.