Leaving aside minor aspects, such as the lack of one or the other member, one finds variations of the following two classifications:
Some authors try to connect the two. For instance, Gāgābhāṭṭa, a late Bhāṭṭa, prefers the first one and asserts that apūrvavidhi can be further divided into classes I to IV. Nonetheless, he further claims that niyamavidhi and parisāṅkhyavidhi are usually (prāyeṇa) instances of viniyogavidhi.
Rāmānujācārya seems to be drawn by a tendency to rationalise the lists and gets rid of the first one, subsuming apūrvavidhi and niyamavidhi within utpattividhi. Parisāṅkhyavidhi is just left out.