Explorer mode the player characters get a stat boost.
Classic mode is the standard difficulty.
Tactician mode
Rhe enemies get a +50% boost to health, armor, damage.
Enemies now regularly start out with 6 or more AP.
Turns are no longer are affected by Initiative scores, but are now hard-coded in a ally-enemy-ally-enemy... fashion.
You are not able to change the difficulty lower on this mode.
Some enemies are supposed to get skill changes and such, but you'll mostly notice that they hit for a lot of damage and are much harder to kill.
It's got some pretty controversial balancing decisions.
Honor mode is Tactician with one save file which gets deleted if your party gets wiped. (Never play this first.)