I don't see a difference. An article 5 convention a convention convened by 2/3 of the states for the purpose of offering constitutional amendments. There are no established rules for conducting or limiting such a convention once it has been convened. Thus, I don't know how you couldn't call it a constitutional convention.
It was suggested you do some research. There are rules for a Convention to propose amendments.
The first rule in a COS is that any amendment that passes must have approval of 2/3s of the states. That is itself is a tight control.
The second rule is that 3/4s of the states must ratify any passed amendment before the amendment becomes part of the Constitution. That is a high bar but not for conservatives. Conservatives still control the majority of the states.
A CC is called to draw up or revise a Constitution. A COS merely amends the existing Constitution if any amendment can get past 38 states.
There is NO CHANCE of a runaway convention. The rules are clear.
The danger from a runaway state initiated amendment convention is also present in runaway congressionally sponsored amendments. Neither has happened.
OTOH, do we not have a runaway, consolidated government in DC?