This is a tricky topic… because I have seen both systems used in music notation, and it has sometimes lead to confusion. There is also the issue of the “non-metered” tremolos as well.
I was always taught that the tremolo slash was a shorthand for rhythmic values. So 1 slash would result in that rhythmic value of the original noted filled in with note values of 1 more beam (e.g., a quarter note with 1 slash would be 2 eighth notes, a half note with 1 slashes would become 4 8th notes, a sixteenth with 1 slash would become 2 32nds, etc.).
A great example is from Beethoven’s Piano Sonata Op.13:
The tremolo on the half notes is represented to divide the half note rhythm in to alternating 8th notes, not quarter notes.
In more recent times, I will say I have seen the idea that 1 slash means to double the value, while 2 slashes means to fill the notes with the note values of 2 additional beams. I think confusion has been allowed to permeate through out the notation community.