State ratifying conventions, which you are correct is the way that the 21st amendment was ratified by the states after having received a two thirds majority in congress: https://en.wikipedia.org/wiki/State_ratifying_conventions
Article V conventions, which replace the legislature stage but then need to be ratified by the states either by the legislatures or by a state ratifying convention: https://en.wikipedia.org/wiki/Convention_to_propose_amendmen...
the latter has never happened and the constitution is very vague about what they would entail, and I think is what the earlier poster was referencing (there has been some recent noise around them)
this graphic is quite helpful: https://en.wikipedia.org/wiki/State_ratifying_conventions#/m...
.png){kind=link}