Learn English – say: “He always goes to cinema this year.”

The time frames "currently" and "at the moment" can refer to a temporary situation, but they can also refer to a situation or action that might continue into the future.

Of the two, I would say that "at the moment" most often refers to a transient or ephemeral action/state, and yet, it most often takes present continuous.

• What is your favorite color?

• At the moment, I'm thinking.

• Who robbed the bank?

• At the moment, we don't have any suspects.

But in some cases (with non-stative verbs) it simply cannot take simple present:

• Where are you going?
• At the moment, I go home (wrong)
• At the moment, I am going home.

"Currently", on the other hand, most often applies to actions or states that are continuing, and might continue indefinitely: :

• Who robbed the bank?
• Currently, we're looking into it.

yet it can reasonably take simple present:

• What inventory valuation method do you use?
• Currently, we use FIFO.

So, all I can say is that your prior notions about simple present vs. present progressive were much too constrained.

By the way, for what it's worth: "currently" extends a litlle into the past, whereas "at the moment" doesn't.

And, as you well know, one can say "I am going to school tomorrow." (But that's a different kettle of fish. Or maybe a horse of a different color. Or, more likely, a fish of a different color—namely, a red herring.)

How about using the present tense to simply describe a current condition or situation?

He is in bed.

They are hungry.

I am fond of answering ELL questions.

and so on. It's the basic use of the "to be" verb, to describe how things are. Moreover, as Peter Shor mentions, you can use the present tense for certain verbs like think, see, hear, feel, want, know, etc. again to indicate a current condition.

I think I will have soup for lunch.

I feel blue.

I see three little birds on my doorstep.

I want a hippopotamus for Christmas.

and so on.