1. Lior your wrong.
2. modern machmir typically means someone who has a yu type hashkafa torah u maada, fully halachic more Zionistic.
3. yeshivish modern yeshivish, yeshivish lite-etc. It usually depends more on someones background. A modern yeshivish brooklyner would prob be considered very yeshivish out of state. A bt who says he’s modern yeshvish is a lot different than an ffb saying it.
Eek you are right, that should be the end of the discussion, sadly in labeling ourselves we forget about Hashem
Theres two hashkafas growing and those not growing.