I know that usually suspensions are referred to by simple intervals, and this is the case with almost all suspensions (4-3, 7-6, 2-3, etc). However, we call it 9-8 suspension instead of 2-1 suspension. Is there a reason for this, either practically or historically?

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This is rooted firmly in the practice of basso continuo, where the figures 2 and 9 had different harmonic implications. The basic idea is that, when a ninth is indicated, the bass is one of the chord tones, and the ninth is a dissonant suspension. But when a second is indicated, it is the bass note that is the dissonant suspension which must resolve downward by step (e.g., what we might call a third inversion seventh chord).

As a typical example, consider Francesco Gasparini's early 18th century continuo manual L'Armonico Pratico al Cimbalo ("The Practical Harmonist At the Harpsichord").

In chapter VII on dissonances and resolutions, he says (square brackets are my clarification):

The second may be considered the same as the ninth, since the ninth is the compound of the second, and because ordinarily one indicates a second [in the bass] and the interval [played] will be a ninth. There is, however, a notable difference between the two, since the second does not derive from, but proceeds to a tie, that is to say, when the bass is tied or syncopated. In this case, the second does not resolve, as do the other dissonances, but instead the bass itself resolves stepwise downward.

Here's a link to the page in question (p. 49), which contains a musical example that better illustrates his meaning: https://archive.org/details/practicalharmoni002034mbp/page/n65

A few pages later (p. 51), he even points out that, if, for some reason, there were an actual 2-1 suspension and resolution, it is recommended to play it an octave higher (as a 9-8), because the resolution to an already-held note doesn't work on keyboard:

If a second is found tied like a ninth, which resolves to the octave, the second should be resolved to a unison. But since the keyboard is not adapted to it, such a resolution would not be heard. For this reason, when such ties are needed (which is rare in harmonic composition) once can use a ninth instead, which is more distinctly resolved to an octave -- as will be seen in the proper place.

Finally, we can compare against his treatment of ninths, where he makes the same distinction, but, I think, explains it more clearly. (p. 60) https://archive.org/details/practicalharmoni002034mbp/page/n77

Even though the ninth is the equivalent of the second, being a compound second, still it is treated differently. It is never used without a tie: in contrast to the second, which occurs over a tie in the lower part (the bass), the ninth itself is tied in the upper part in order to be resolved to the octave.

Once again, there is an example to demonstrate his meaning.

Since this answer received some additional attention recently, and has an incoming bounty, I decided to create a little example of my own to compare the difference between 2nds and 9ths. At each of the first three barlines, there is a C in the bass voice against a D in the soprano voice.

At the first and third barlines, the bass is suspended while the soprano moves to the D, so the interval is considered a 2nd and the bass must resolve downward by step while soprano voice holds the D. However, at the second barline, the soprano's D is suspended while the bass moves, which means the interval is a 9th, and the soprano must resolve down stepwise.

  • (Also, notice the difference in the chords that accompany the 2nd's, and the resulting harmonic implications: the 5/4/2 implies the bass is a suspended fourth, while the 6/#4/2 implies a 3rd inversion dominant 7th chord, and creates a modulation to the dominant, which I reinforce with a cadence)

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