What's the difference between "right now" and "currently"?

They are almost the same, usually interchangable, but in certain contexts they might be interpreted slightly differently depending on the listener/reader.

"Right now" could be interpreted as meaning "in this instant", or "at this very moment". Whereas "currently" is still referring to the present, but a present that is still ongoing, possibly for a longer period than "right now".

For example:

"No thank you, I don't want coffee right now" - meaning, I don't want a coffee now at 11.03am, but I might want tea at 11.57am.

"No thank you, I don't currently want coffee" - this could be interpreted as meaning I don't want a coffee at all, because I am having a day/week/etc of not wanting coffee.

Other examples

"Syria is currently at war" is probably more appropriate than "Syria is at war right now" as it better reflects the 'ongoing' nature of war.

"I am on the phone right now" seems less formal than "I am currently on the phone".

The only time I can think that they are not interchangable would be when giving a command:

"We need a doctor, right now!" sounds very urgent. "We need a doctor, currently!" - implies that we do need a doctor, but it's possible we already have one, the task is ongoing... it just doesn't convey the same sense of urgency.

Right now seems to have more more contrastive emphasis than currently. It contrasts with other times. Otherwise the meanings are fairly similar. However, their grammar is not at all similar in any way. There are very many situations where it is ungrammatical to use currently but grammatical to use right now.

The reason for this is that right now is a preposition phrase, and currently is an adverb. We can use preposition phrases as well as adverbs as temporal adjuncts in sentences:

• I am working right now.
• I am currently working.

However, there all grammatical similarity ends. We can use preposition phrases to post-modify nouns, but we can't freely do this with adverbs:

• The concert right now will be better than the concert tomorrow.
• *The concert currently will be better than the concert tomorrow.

And we can use preposition phrases as Predicative Complements, but we can't do this with adverbs:

• *The meeting is currently.
• The meeting is right now.

Notice that right now is a preposition now modified by the specialised adverb right. This adverb can be used to modify prepositions, but not adverbs (in standard English):

• right now
• right through
• *right currently
• *right locally

In short, although the meanings of right now and currently are very similar, their grammar is not!

This is a good question, because currently is somewhat elusive to define, as you have no doubt seen by googling for it, and right now is only subtly different.

Meaning:

Currently refers to something that is true now, and in an ongoing sense, but is not expected to be permanent.

Currently we are having a hot spell.

... the weather is hot, but eventually it will change.

I'm currently not at my phone.

... and later I will be back and will listen to your message

Right now focusses more on the exact moment, and has more of an implication and expectation of change.

Right now it is too hot to go outside

... but soon, in the evening it will be fine.

I can't talk right now

... I'll get back to you as soon as I can.

(Note: later answers have correctly pointed out that "right now" can bring an element of imperative that "currently" does not).

Grammar:

There is a grammatical difference between the two.

Currently is an adverb. It describes something taking place (verb).

Right now is a noun - it is a time.

So they can be used interchangeably in sentences, but not without slightly changing the sentence (usually) to accommodate this difference.