Proofread / Check / Copy-edit / Edit / Revise

Hello,

What would be the difference between checking and proofreading? (see: [url]http://axiolexis.ro/[/url] ) My guess is that when something is proofread only spelling and grammar are checked, while when something is checked, as the OED definition below says, more than the spelling and grammar are checked, maybe style and something else.
Moreover, how correct is the word “copy-edit”? Thesaurus.com provides it as a definition for “proofread” (see: [url]PROOFREAD Synonyms: 15 Synonyms & Antonyms for PROOFREAD | Thesaurus.com).

OED ([url]Oxford Languages | The Home of Language Data)
• proofread: read (printer’s proofs or other written or printed material) and mark any errors;
• check: examine (something) in order to determine its accuracy, quality, or condition;
• copy-edit: edit (text to be printed) by checking its consistency and accuracy;
• edit: prepare (written material) for publication by correcting, condensing, or otherwise modifying it;
• revise: reconsider and alter (something) in the light of further evidence;

Thanks!

‘proofreading’ is a specialised form of ‘checking’.
You can check things other than the printed word. You can only proofread the written word.
Proofreading can include checking for style, fluency, etc.

I won’t dispute the ‘correctness’ of words provided by a reputable dictionary.