Proofreading eliminates language errors and errors in punctuation, grammar, spelling, format, and style to improve the readability and clarity of text.
Text correction involves checking and correcting typographical, punctuation, and spelling errors as well as other minor mistakes (“typos”, etc.). It is usually applied to already translated and proofread texts prepared for printing.
Text editing involves making revisions to and checking the content and the specialised terminology of a text, in addition to correcting spelling and grammatical errors.