The Way of Mercy Monk's Hand of Harm feature says:
When you hit a creature with an unarmed strike, you can spend 1 ki point to deal extra necrotic damage equal to one roll of your Martial Arts die + your Wisdom modifier.
However, the Way of the Kensei Monk's "One with the Blade" feature says:
When you hit a target with a kensei weapon, you can spend 1 ki point to cause the weapon to deal extra damage to the target equal to your Martial Arts die.
This second feature notably lacks the phrase "one roll of". Now, I've ruled that One with the Blade adds damage equal to a roll of the Martial Arts die, but I've got a player that insists that the intent of the feature is to add the maximum damage of one roll to the hit. So in our case instead of adding the result of 1d6, they insist that it is supposed to add a flat 6 every time they use the feature. They cite the argument "if Wizard's intended the features to do the same thing, they would use the same words, so obviously they are supposed to be different."
So what I don't need here is "just rule it how you want" or something to that effect, because that's what I have done and everyone is okay with that. That's the solution I have already implemented and it has worked out just fine. What I would like from answers is a more rules focused justification for my ruling (or, of course, rules focused objections to it), if only to satisfy my general desire to be consistent with the rules as written.
Best Answer
They have the same meaning
Firstly, "damage equal to one roll of your Martial Arts die" is rather straightforward in that you actually roll the die. And then we must examine "damage to the target equal to your Martial Arts die."
Looking at the Martial Arts feature itself we see that it says the following (emphasis mine):
The Martial Arts die is, itself, a die. It is not a number, or this sentence wouldn't make sense. Thus we can translate "damage to the target equal to your Martial Arts die" as "damage to the target equal to a d4" (or another die). If they wanted it to mean the maximum of your Martial Arts die, they would have used the word "maximum" or something similar to what they do with Hit Dice:
Furthermore, different features using different wording is not evidence that they must mean different things. The writers and editors are human, so they will make mistakes, but more important than that is the fact that 5e is written using natural language, so while features may try to have consistent wording between them, they do not need to be worded consistently because so much of their descriptions consists of non-game-defined terms.