"Diminutive" form usually means part of a word is added or changed .. like adding "et" to Jane to get Janet or Janette. Janelle, too. It also describes names like Jamie, diminutive of James.
In some languages a diminutive has a definite form, like -ita or -ito in Spanish, or (I think) -an in Irish (see the entry for Ryan), which changes the meaning of the name from [meaning] to "little [meaning]".
Diminutives and pet forms are not readily distinguishable in English. At least not to me.