Ive see the trend of certain MAME year versions become some kind of marking point for emulation. but after MAME 2016 which is next version to become a staple. The others after 2016 I only seen labeled as MAME Current.
MAME 2003 (aka 0.78) was around when og XBOX homebrew emulation was starting to become popular so i assume most people just ended up testing that version and it became the standard for the console.
MAME 2000 (aka 0.37b) which you forgot to mention is another one that became a stop gap. It’s an older version that, again, was used for the og XBOX. The reason was that 0.78 was too slow with some Midway boards like Mortal Kombat and NBA JAM. AFAIK, 0.37b was the last version before some accuracy improvements made these boards slow to emulate on XBOX.
MAME 2010 (aka 0.139) was the version that was around while smartphones were starting to get into MAME emulation. Again, i assume most people ended up using that one, just like with 0.78 and XBOX. Android MAME standalones are based on that romset. Not sure if there is any other technical reason behind it. So it’s the romset most people are using for Android devices and phones.
I think there is a also MAME 2015 romset that gets maintained. And while i’m not sure, i think that one must be the last version before MAME got merged with MESS that year, so it makes sense to keep the last “clean” version.
As for MAME 2014 and 2016, i’m not sure. Maybe they were just “stop gaps” for people who wanted a newer, more accurate version and stay with it for a while because updating your MAME rom sets is a pain in the ass. I was set with standalone version 2016 for quite a while myself and even asked for someone to compile it as a separate core from the “current” one in these forums.
I guess this trend is over now as performance isn’t a factor anymore, if your device can handle MAME 2016, it should be able to handle the latest version anyway.