Lets go back a bit to start with.
Asheron's Call, Everquest 1, Ultima Online...they were real MMOs. No instances, no tiny 6 player co-op groups (which isn't massively multiplayer) and everyone was part of the same world.
Today, only EVE Online and Black Desert Online and maybe a couple others fit the classic definition of MMO. No instances, can see 1000s of players around you and you can have TRUE massively multiplayer sized groups (at least for EVE). There is no shared instances, everyone is part of the same experience. Like look at GW2, it even tells you to switch instances if the instance you are in has lost too many players...that is a shared world.
Shared Worlds however fit better for most modern MMOs.
Games that fit the definition of Shared Worlds (that are relatively modern) is FFXIV, GW2, WoW, SWTOR, ESO as just many examples.
In WoW, the vast majority of your time are in 6 player sized groups and spending time in instances. Also, in WoW you aren't part of one server but multiple instances of various servers and that makes WoW the ultimate example of a game that shouldn't be considered an MMO but a Shared World.
FFXIV/GW2/SWTOR/ESO also all have instances and tiny groups. They all focus heavily on soloing, or co-op experiences. All have Co-op experiences (again like WoW has 6 player sized groups, that is a co-op experience). Games like ESO/SWTOR heavily focus on soloing most content, and the people around you could just as well be NPCs...a very fitting description of Shared Worlds. SWTOR especially is solo only from level 1 to max level, and you only share the world with others but with very limited interaction.
This solves the debate of what an MMO is and is not. Many games fit the Shared World definition, but very few games fit the classic MMO definition. In old MMOs, instances, shared servers and multiple "channels" of the zone you are in and tiny 6 player sized co-op groups was unheard of. All that makes the game a shared world. But EVE Online is truly open with no instances, huge massive groups and everyone takes part in the same server (in fact there is only 1 server) and that makes it a true MMO, and any MMOs like that a true classic MMO. Most new games are more Shared Worlds however than classic MMOs.
This should make everyone happy on all sides of the debate.