Yes, the author refers to it by both names. Since I don't use its stats-gathering capabilities, I have not held onto that part of the name.
I'm not sure what you mean by this. Background-only status? Different circumstances?
Yes, this AppleScript:
tell application "TextEdit"
set winNameList to name of every window
end tell
return winNameList
will do the job, mostly, but it's all one line with comma-space delimiters and I have numerous files where I use comma-space in the file names, so a little more complication is necessary, as in this example from @ComplexPoint:
How to List All Windows of One App That Are Open in All Desktops - #44 by ComplexPoint