word choice - "has been completed" or "is completed"? - English ...
passive voice - "Testing complete" vs "Testing is completed" - English ...
"Complete" indicates a thing that has been finished. "Completed" is a past-tense verb form, and while by itself means much the same thing as "complete", it has the additional implication of something that has been finished, and as a consequence, the word has additional implications of the process that completed the thing. I would go with ...
This perhaps reflects a distinction between finished as meaning "got done with" and completed as meaning "made whole": the author can be understood either to have got done with writing the novel or to have made the novel whole; but the reader can be understood only to have got done with reading it.
Complete: fully constituted of all of its parts or steps, fully carried out, or thorough. Completed: to bring to an end or a perfected status. Therefore, something is complete, or something has been or was completed. However, in a lot of cases, you can use either. In your case, I would use completed, to be consistent with the other terms you used (queued, started, finished...), and it sounds ...
Your two examples Repeat the steps for the next weekly report until the monthly report has been completed. Repeat the steps for the next weekly report until the monthly report is completed. are essentially equivalent both saying to complete the monthly report. A slight nuance might be that since perfect tenses imply an ordering of events, your first example leaves the listener expecting ...