The connection between Monk and Tatum would be worth while following up. These are the main similarities in their solo styles:

Reliance on stride patterns. Both play the melody of the song, with only melodic paraphrase and ornamention. Neither just blows over the changes like Bud Powell.

Breaking the stride pattern through heavily ornamented and rhythmically irregular playing, rubato.

Some similarities in ornamention: use of runs.

Use of dissonant or colorful chords; imaginative reharmonizations.

Preference for standard tunes. (Check to see what tunes were recorded by both; see if Monk refers to any of Tatum's ideas while playing "Tea for Two.")

The differences:

A different touch on the piano. Tatum's more fluid, virtuosic, and conventionally pianistic. Monk's percussive and unconventional.

Monk will often play a standard tune more "ironically," with the feeling of playfully going back in time, as in his reading of "Dinah." In fact, it is mainly the difference in epoch (though these overlap) that defines their differences.

You could also point out that Monk's rubato is not Tatum's rubato. Monk creates a kind of uncomfortably hesitating quality that is foreign to Tatum. Despite the similarities it would be hard to confuse one pianist with the other.