In addition to Lynne and Jim's comments..... there are some huge differences.
Cavern and wreck dives essentially use the same motor skills - but the environment is vastly different.
Some of the key differences are:
1. You often have to enter a wreck through a restriction (e.g. a window) that necessitates skills that you may not have covered on your cavern course - air sharing through a restriction. Unfortunately, air sharing in the overhead environment is explicltly excluded from the PADI Wreck course - it's that reason alone that I wrote our Advanced Wreck course.
2. Whilst penetration distances may be shorter, total distance to the surface is often greater.... in the sense that many caverns are relatively shallow or even have entrances that occur at the surface. Air sharing is relatively straightforward, where as wrecks require to first get out of the wreck (see above) and the potentially manage an OOG ascent from 30m+.
3. Wrecks are, in their own way, more fragile than caves. For example, the first trip I did to the Mikhail Lermontov I used a single finger to steady myself - I pushed it right through the (rusted) steel plate. They are also fragile in the sense of artefact removal - something that cave divers would never dream of doing, yet our martime archealogical heritage is regularly plundered by people with china fever.
4. Variability is huge - as beams rusted and rooms collapse, the change from dive to dive can be quite pronounced.
5. You don't always know where the entrance is on a wreck - so navigation and identification of suitable penetration points is a key skill.
My list does go on for several pages - but I won't bore you with the details. I think it's fair to say that you'd not get a tenth of the skills/knowledge you need from a bog-standard PADI Wreck Diver course. The fact that air sharing in the overhead is precluded is the one reason that I would suggest not doing it but looking for alternatives.
