All three end with your data safe somewhere else. They differ in how much is copied each night, how much space is kept, and - the part that matters when you actually need it - how many pieces have to be present and intact to restore.
Full
Everything, every time. Slowest to take, largest to keep, simplest to restore: one archive, and it is complete on its own.
Incremental
What changed since the LAST backup of any kind. Fastest and smallest. To restore you need the last full backup plus every increment since, in order - and if one of them is missing or corrupt, everything after it is unusable.
Differential
What changed since the last FULL backup. Grows through the week, but a restore needs exactly two pieces: the full backup and the latest differential.
Which to choose
- Small site under a few GB - nightly full. Simple beats clever, and simple is what works at three in the morning.
- Large site, plenty of change - weekly full, nightly incremental, and test the chain.
- Large site, awkward restore window - weekly full, nightly differential. You trade space for a two-file restore.
What modern tools actually do
restic, borg and similar are incremental in what they transfer and behave like a full backup at restore: every snapshot is browsable and restorable on its own, because the pieces are deduplicated rather than chained.
restic -r /srv/backup backup /var/www # transfers only changes
restic -r /srv/backup snapshots # every one is complete
restic -r /srv/backup restore latest --target /tmp/check