Sadly, best answer is: "Depends on specific company" I will describe you, how I do it in our little group of fandom newspaper which we publish just for fun:
Roles:
1) Head editor: Agrees of content of the whole new edition (new issue of the magazine), agrees on timelines (who delivers what and when), is responsible for overall look and structure of the new issue. in our case also puts the final issue to the print
2) Writer: Writes the agreed content
3) Editor: Checks the content of the article. Fixes tpyos and grrrammmatycal isssues
Process:
1) All agree on what should be written (Pavel doees the interview, Alice does the article on X and Bob delvers the funny story)
2) Writers submit they work for peer review: Every writer submits their first version. Everyone then has a discussion about the article (Pavel, you should also ask about the hedgehog!)
3) Once peer reviewed, writer tweaks on their story and submits new version to peer review
4) Once everyone (or most of the group) agrees on the article is final, the article is sent to editor
5) editor check the article for grammar issues and after finished, sends back to head editor
6) Head editor puts all articles into issues and posts first version of whole magazine (PDF file) to peer review. Everyone checks for layout issues, left out typos and overall look and feel of the magazine
7) The whole magazine issue goes through tweaking and peer review once all (or most of the group) agrees on the whole issue is final.
8) new issue of the magazine is published
Side note: We publish four issues a year, so we can afford having quite thoughtful process. And obviously, one person can have two or more roles