Levitate is a spell that allows the caster to control the elevation of a target. To quote the rules:
You can change the target’s altitude by up to 20 feet in either direction on your turn. If you are the target, you can move up or down as part of your move.
The Player Handbook has this to say about multiple movement speeds:
If you have more than one speed, such as your walking speed and a flying speed, you can switch back and forth between your speeds during your move. Whenever you switch, subtract the distance you've already moved from the new speed. The result determines how much farther you can move. If the result is 0 or less, you can’t use the new speed during the current move.
Assume that I have cast levitate, landed at some point, but am still concentrating. If I use all of my 30 walking speed, am I prevented from ascending using levitate, or is the movement granted via levitate different than other movement speeds?
Best Answer
Levitate doesn't give you a different Speed
The spell Levitate permits you to move yourself in a way you couldn't before. Specifically (PHB, p. 255, bold added):
This may sound like it gives you a "levitating speed" of 20 feet, but the spell does not specify that it does this. Contrast that with the spells Fly or Gaseous Form, which state:
In the absence of similar text in the Levitate spell's description, we must conclude that you don't gain any new speed from Levitate. Instead, Levitate does exactly what it says it does: it allows you to move up to 20 feet in either direction "as part of your move."
What difference does that make?
So we've established you move via levitation "as part of your move." What does that mean practically? The rules on movement state (PHB, p. 190):
In your given example, a character who has walked 30 feet this turn (their speed) is under the influence of the Levitate spell (which they cast), and wants to immediately levitate upward. But since they've already moved "up to their speed" they cannot move further "as part of their move" this turn (unless they take the Dash action or otherwise give themselves additional movement). Thus, in your example, the character would be unable to rise, but not for the reason you suggested (having to do with multiple speeds).
Note that this can also work in your favor. If you moved 20 feet on the ground and then used your movement to change your altitude via Levitate, you could raise or lower yourself 10 feet with the spell (assuming your walking speed is 30). This would have been impossible if Levitate gave you a new speed (which, again, it doesn't), since you would subtract the 20 feet walked from the 20 feet "levitation speed" and find yourself unable to move via levitation at all that turn (due to the rules on moving with multiple speeds which you quoted in your question).
The difference between "speed" and "movement" is complicated, and this is one of the more sticky examples of them interacting in strange ways. But the bottom line is that you don't have to worry about the rules on multiple movement speeds when using this spell because the Levitate spell doesn't give you a different speed.