What are the differences between Story Mode and Speedrun Mode?

I've played through Rabi-Ribi a couple of times in various difficulties with various objectives. I was planning to attempt getting the Speedrun achievements next by completing the game in Casual Alternative mode and then starting a New Game+ to attempt the actual speedrun in Loop 2 (as suggested in the comments on this page).

A few minutes into the game, I started wondering if I should have started it in Speedrun Mode rather than Story Mode, mostly to make my save files easier to identify. This raised the question: Is there any major gameplay difference between the to modes?

I've only looked into speedrun mode for a short amount of time, and so far the only differences I noticed are that it auto-skips cutscenes and displays a timer and keeps track of your completion stats at the top of the screen. Does anything else change, or does this mode only make things more convenient for speedrunners?

What I'd like to know is if I can still get regular achievements in speedrun mode, and if I can keep playing it after the post game is completed (to start a New Game+, among other things).