I'm old enough to remember these terms developing. I can remember when the first Diablo came out and called itself an 'ARPG'. There was some controversy over this term and simply the use of the term RPG. As video games developed, there was some prestige around the 'RPG' label. By the late 90s, you were looking at a lot of well loved and top games using the term. Gold Box Games, Bard's Tale, Ultima, JRPGs like Phantasy Star and Final Fantasy, Dragon Warrior, etc.

Diablo is the first game that I can recall that really prominently advertised itself as an ARPG. They did this of course because it wasn't really as deep as the rest of them. There weren't a lot of 'choices' to be made in this game. You set up your character and ran through the dungeon. They wanted to use the 'RPG' label because it was well regarded at the time and helped move units. It was a lot like calling an RV a sports car because sports cars have wheels, doors, can drive on the road. ARPGs had RPG mechanics, in that there were things like stats and you could choose abilities/spells on level up. But they really weren't RPGs.

Around that time in PC Gamer there was a great column about what made an RPG an RPG and it was clear that games like Diablo weren't it, the key from that was an RPG had players making meaningful choices that had a lasting impact on the game world. Whether you threw fireballs or lightning bolts wasn't exactly a meaningful choice that had impact on the game world.

When it came to JPRGs vs RPGs, the difference was always fairly clear. RPGs were of the D&D variety. While they featured magic, the system itself was somewhat grounded in reality. JRPGs had a distinct style. Big numbers, wild combos, certain aesthetics, etc. To me the JRPG label makes sense, because it is a different style of game. I would note that JRPGs though really didn't fit the definition of RPG for the most part, a lot of 'RPGs' didn't because there was very little decision making. They were quest style games where you had a party that levelled up, but you weren't making many decisions in the game that had much an impact.

I think the labels are absolutely important for distinguishing the type of game it is. People want to know what they're getting into when they play it. If I'm expecting Baldur's gate and get Diablo, I'm probably going to be a bit disappointed.