Classic feel. High lethality, combat as war, dungeon crawling, random encounters, shenanigans abound, etc.
Modern feel. Story focus, low lethality, character builds as a pillar of play, combat as sport, etc.
Classic design. Discrete subsystems abound, use all the dice, etc.
Modern design. Unified resolution system, lack of discrete subsystems for various skills and abilities, clear and concise explanation of rules, etc.
OSR. Classic feel...classic design. OSRIC, Old-School Essentials, DCC RPG, etc.
NuSR. Classic feel...modern design. Shadowdark, Dragonbane, X Borg, etc.