PRESENT CONTINUOUS

I have a question about a "time word" that I saw with the present continuous--today. My understanding is that the present continuous is used to express an action executed at the moment of speaking, and it can also be used to express futurity. I feel that when somebody asks the question, "What are you doing today?" This person is asking about what one will do ( futurity) at a later time that day, as opposed to what one is doing at the moment the question is being asked. This is how I am interpreting this question because of the "today" in it.

I think that if I want to use the present continuous to ask about or express an ongoing action, I would substitute "today" for "at the moment," "right now", and "now" since these time words TRULY express ongoing action and they are used more often for this purpose, in my point of view. Am I correct in my interpretation? Please enlighten me.