I don't think you'll find any consistent use of terms in the field.
I recall that when The Method emerged, people were hurling out things that had the equivalent of a ball of groundbait moulded around a weighted frame, and a Method Feeder Rod was a beefy affair. But things are relatively refined in these days of mini hybrids etc.
A glance at some big brand's rod labelling shows the language is all over the place.
Drennan's Red Range Carp Feeder rod comes with lighter tips (2,3oz) than their Red Range Method Feeder Rod (3,4oz).
Shimano call everything in the leger dept a Feeder Rod - including their two Winklepickers, traditionally, the lightest of light bomb rods. Go figure.
Daiwa call nearly everything a Feeder Rod, then suddenly label a budget range Method Feeder Rods, although their specs are no different, and even offer a Mini Method Feeder which has the same specs (line, casting weights) but is shorter.
Browning have a Carp Wand Feeder Rod ........
Ignore the labelling. Check the specs for individual rods or the rods themselves if buying. And do what you do - match your rod to your fishing that day.