That's the nature of MIDI files. They don't encode audio, they encode a set of instruments with a list of notes. It's up to whatever's playing them to provide what those instruments actually sound like.

Here's an example of the same MIDI file being played back on several different devices: https://youtu.be/eiMP-PlL6VM?t=954 It's clearly the same song on all of them, but it sounds slightly different.

Modern browsers do not support MIDI playback on their own, so chiptune.app is presumably doing it on its own with its own (likely intentionally retro) sound font providing the instruments.

Additionally even if macOS had its own system-level MIDI synthesis (not sure if it does), GarageBand would actually probably still be different since it's main purpose isn't MIDI playback -- it's to be a DAW.

MIDI does not have a sound. It's just instrument data. The classic "MIDI sound" that you recognize is the Roland GM soundkit shipped with Windows (an early version of Roland's Virtual Sound Canvas product).

This website uses a different instrument set. You can actually select which one it uses in the Settings panel, but by default it uses Kenneth Rundt's GMGSx.sf2 (which does sound quite a bit Roland-y to me), as shipped by SynthFont.

I don't know what instrument collection GarageBand uses.

MIDI files only contain a description of (simplifying somewhat) the rhythm and base pitch of notes, and which instruments they should be played on, so the realisation can vary drastically depending on the particular system and configuration (e.g. soundfont choice) it's played back with.