binding catbag and a special trick before a run doesnt make it ng+ tho, if it was ng+, you wouldnt do the last mission of the game "erics line". there was a reason for thug2 separating the ng and ng+ categories but all of the runs on the thug1 leaderboard are ng so there is 0 reason at all why there would be a ng+ category on here lol
It's mostly the games structure that's the difference. THUG1 allows you to modify everything on a clean save file, special tricks, catbag and all that. Because you start in an actual level(NJ), you can reload saves with little discrepancy. Along with the fact that apart from reduced RNG and maybe more leniency on the buttslaps you can get, doesn't affect the run as much compared to not having catbag.
THUG2, you spawn in a tutorial level that doesn't count towards any game progress so we just start timer from selecting Boston from the change level menu. Also, hitting new game clears all your equipped specials and tricks. With story and classic mode, you're using a save file with moves you got from playing a different mode (some form of game progress). Story = Hot Rod (Classic Mode Sick Difficulty), Paulie Butt Manual (Story Mode Normal) or Classic = Everything above + unlocking tagger in Berlin for Double Fistin' (AND boosting your story stats to max to benefit classic skater's performance in that mode).
tl;dr THUG1 is mostly speeding up certain goals but it's mostly still a linear route and equipping isn't as controversial as a process as THUG2 based on quitting out and saving a file with game progress already on it.