Right away 🆚 Right now

Both of these expressions mean "immediately", but "right away"  means  "without delay" and tends to be used in situations where there is worry or urgency, in situations where there is really not a moment to lose before some bad thing might happen.  

▪️ We took him to the hospital right away.
▪️ I need you to print these documents right away, so we can use them during the meeting.
▪️ I'll make sure to compelete the notes right away.

"Right now", on the other hand, is often used in angry/annoyed/formal imperatives (telling someone to do somethng), as in:

▪️ You're late! Come to the meeting room right now!
▪️ Finish it right now!

Another very important difference between these expressions is that "right away" can be used for actions in the past or future whereas "right now" really means "right now" = right after the moment of speaking.

✅ Yesterday after the meeting, the client asked to send the report and we did it right away.
❌ Yesterday after the meeting, the client asked to send the report and we did it right now.

✅ I'll send the email right now.
✅ I'll send the email right away.

Sometimes "right away" and "right now" can overlap.  

✅ I have to go right now!
✅ I have to go right away!

There is still a slight feeling of difference, though.  

✅ I have to go right now! Or I will miss the last bus. = I have to leave this VERY MOMENT, right NOW.
✅ I'd love to stay longer but I have to go right away!  = I cannot do what we're doing any longer and I have to leave.

👉right now ➡️ more argumentative, assertive, or insistent in tone / formal
👉right away  ➡️ more simply informative / casual