The question revolves around 'right?' at the end added when the speaker is not sure about her/his understanding.
I think it is common to use "..., right?" where "..." is the speaker's understanding (of the topic under discussion) while it is possible to use correct in the same way.
Do right and correct make the sentence(s) sound different in formality or implied attitudes of the speaker?
A related question is about right/correct for answering. Does it make any difference just to say "(That is) Correct." or "(That is/That's) Right." as a response to a "..., right?" statement?