What makes a sonnet? For most early modern examples, the answer is clear: a 14-line rhyming poem, its form either Shakespearean (three quatrains and a couplet) or Petrarchan (an octave and a sestet). There are exceptions to those formal rules, but most sonnets meet them.
Formal rules are the conventional answer. And that answer works for conventional sonnets, which are the vast majority of sonnets.
But if you enforce formal rules too rigorously, you encounter a few interesting problems. These are the problems that my project is investigating. Moments’ Monuments: The ACL Database is collecting as many sonnets as possible, so I can get a more definitive answer to this question: Is the sonnet a form or a genre? The trouble is, you need to decide first what qualifies as a sonnet.