As others have said, they are just mono PCM samples in 8-bit signed format, length up to 128k (minus two bytes, as maximum is 65535 words).
What makes them "instruments" is the fact that you can specify a sample volume, sample loop points and note pitch fine tune values (in addition to a sample name).
IIRC, the "funny" base sampling rate for a 261.6 Hz C-2 note (actually C-4 on a piano) comes from some programming examples, where a 32-sample sine wave was played at 261.6 Hz, and this note required the sound hardware period value to be set to nearest integer value of 428, and 3579545 (sound chip clock for NTSC Amiga) divided by period value 428 is 8363.4 Hz. Those programming example values for notes were just used as is in mod players.
Drum samples were usually played with higher notes than C-2, maybe at note A-3, because it was the highest standard note the DMA hardware could play back without skipping samples.
I think by using finetune to speed up a bit it's still possible to play samples a bit faster without skipping, maybe up to A-3 with finetune +3.