Contract drafting is a process where in the drafting person will draft a contract from the starting point (Title of the Agreement) to the end point (Miscellaneous segment/signature block).
In contract vetting process, drafting person will be a reviewer and will just work on the existing contract template (which is already drafted one) to do the requisite additions and deletions in the existing contract template.
Professionals working in certain companies will have the opportunity only to vet the contracts for two reasons:
a) Either such companies will have their own contract templates; and
b) Counter party will send their contract template for review.
In vetting process the learning curve will be limited for professionals as they will have to focus on specific pointers in the existing contract template and do not get the prospect to do the first hand work.
On the other hand, in the contract drafting process the drafting person will draft the entire contract on his/her own with specific focus on each and every minute point from the starting point to the end point .
Contract drafting will provide the drafting person with the opportunity to learn the art of drafting provision by provision and leave the window for a full research on different clauses to learn each clause to its core.
I personally suggest the young legal minds to focus on learning contract drafting (to learn first-hand work) to the core to be proficient in contract drafting or contract vetting.