This may help.

correctly / incorrectly

You spelled the word correctly.
You spelled the word incorrectly.

The music was correctly printed.
The music was incorrectly printed.

Did I say it correctly?
Did I say it incorrectly?

You answered every question correctly.
You answered every question incorrectly.

right / wrong (adv)

You spelled the word right. (=You spelled the word in the right way.)
You spelled the word wrong. (=You spelled the word in the wrong way.)

The music was printed right. (Not "right printed")
The music was printed wrong. (Not "wrong printed")

Did I say it right?
Did I say it wrong?

You answered every question right.
You answered every question wrong.

right / wrong (adj)

It was right for you not to invite them.
It was wrong for you not to invite them.

Did Jack get up on the right side of the bed?
Or did he get up on the wrong side of the bed?

When you first meet someone,
it's good to start off on the right foot.
it's not good to start off on the wrong foot.


rightly / wrongly

These are usual before a participle. They draw in a shade of meaning more than mere correctness and incorrectness. They imply "just", "honest", "proper", "suitable", and their opposites.

He was rightly accused of theft. (shades toward "justly")
He was wrongly accused of theft. (shades toward "unjustly")

He was accused of theft rightly. (?)
He was accused of theft wrongly (?)

Society rightly fears the spread of drugs. (It is right/suitable/proper for society to fear the spread of drugs.)
The authorities have wrongly imprisoned the man, as DNA tests will show.
(It was wrong/unsuitable/unjust/improper for the authorities to imprison him.)

"wrongly" occurs frequently in matters of criminal justice:
wrongly accused, wrongly arrested, wrongly convicted, wrongly imprisoned

When you say "The page was printed right", you mean that the page was printed correctly.
When you say "The page was rightly printed", you mean that it was proper to print it; printing it was the correct thing to do.

> I think you mean "Do these words differ in meaning?"
Yes, my silly mistake.

To confirm, do you mean incorrectly and wrong have the same meaning?