Proofreading is restricted to checking and correcting formal aspects, such as punctuation, spelling, grammar and layout. Classic proofreading is mostly suitable for texts that have to be checked one last time in the final layout before they are published.
Linguistic editing goes into more depth. If you have your text proofread by Interlingua, then the proofreader will also make additional stylistic suggestions for improvement. This service is mainly suitable for making sure that the text is pleasant and easy to read.