Article V reads (italics added):
The Congress, whenever two thirds of both Houses shall deem it necessary, shall propose Amendments to this Constitution, or, on the Application of the Legislatures of two thirds of the several States, shall call a Convention for proposing Amendments, which, in either Case, shall be valid to all Intents and Purposes, as Part of this Constitution, when ratified by the Legislatures of three fourths thereof, or by Conventions in three fourths thereof, as the one or the other Mode of Ratification may be proposed by the Congress...,Provided...that no State, without its Consent, shall be deprived of its equal Suffrage in the Senate.
However, that did not stop a stipulation in New Mexico state law that provides that members of that state's legislature would themselves make up such a convention, if Congress again selects that ratification method.
"the nominating petitions shall contain a statement as to each nominee, to the effect that he favors ratification, or that he opposes ratification, or that he will remain unpledged, and no nominating petition shall contain the name of any nominee whose position as stated therein is inconsistent with that of any other nominee as stated therein.
Also, such a ratifying convention is different from a constitutional convention insofar as the latter term is sometimes understood to designate an assembly whose purpose is to write an entirely new constitution for the country as a whole.
The U.S. Constitution, unlike of some of the states' constitutions, contains no specific provision for a national convention that would completely replace the existing constitution; however, a national convention called to propose amendments under Article V could theoretically propose (an) amendment(s) which would be tantamount to an entirely new constitution—but even an entirely new constitution would subsequently require ratification in three-fourths of the state legislatures or by three-fourths of the conventions held within the states with Congress choosing which option to use, as Article V of the current document demands. It's notable that under Article 5, even a convention could not propose a new constitution that would deprive each state of its equal membership in the Senate without the state's consent. It is noteworthy that the present constitution was proposed by a convention originally called to do nothing more than to amend the Articles of Confederation. See Convention to propose amendments to U.S. Constitution