It is hard to say, it would depend on the context. A violation could be a charge, or a ticket, or a violation of probation or some term of release. A conviction means specifically that the person was convicted of a crime. Some people might use violation to describe a conviction. It really depends on the context and how it is used.
In Washington state, it's common to find probation or SOC terms that specify "No Criminal Law Violations", or NCLV. This is typically read to mean "No Criminal Law Convictions" and most courts in my experience have not violated persons who have been acquitted or otherwise had new pending criminal cases dismissed on the merits (as opposed to another SOC or other "disposition"). But you should read your conditions carefully, because some courts are inserting the alternative language "no arrests or criminal law violations".
You should ask your attorney to clarify this for you to be sure.
Interesting question. Prosecutors will argue that one violates his/her sentence is they recieve a criminal "violation." Usually this means being chraged with a crime. Some judges will sanction a defendant for a mere violation - really the appearance of commission of a crime - even though no conviction has been attained by the prosecuting authority. A conviciton, of course, means an actual finding of guilt, which almost assuredly means sanctions for violating theterms of sentence.
I agree with my colleagues here: the terms depend on the circumstances surrounding them, and you should speak to your attorney to clarify the language.