Quite similar in that they can both be used to mean that something was done in a way that was not accidental. However, "deliberately" can also mean that an action was done carefully with, say, every step of the action in mind as it is being performed.

There are not any significant differences other than the fact that in law, „intentionally“ is used more often than „deliberately“ but I really don’t know why. It might be because „intentionally“ contrasts better with its opposite, at least in the legal sense, of „negligently.“ It may trace to the „mens rea“ concept of the intentional act as a mental state of mind, which is a necessary element to prove in many crimes, while negligent acts are often not criminal or only occasionally treated as such, depending on the circumstances.

Intentionally and deliberately mean the same thing. It means that a person did something, and that it was not an accident.

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