Different Color Results, "Same" Document Color Profile
Hello. I'm experiencing something I haven't come across before. I'm working in two different Illustrator files. Both seem to me to have the exact same color profile set up (see image below). For both documents, I've selected sRGB IEC61966-2.1. However, on the bottom of the program, where I've chosen to show the document color profile, one file is stating it's actually "Display" (see images below).
I'm working on establishing brand colors and need to know how to reconsile this issue.
As an aside, which color profile should I work in while establishing brand colors? We're a tech company and primarily promote online so I'm looking to establish accurate colors for web.
Thank you in advance for your help.
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Both files have these color settings:

One file (the file with duller colors) shows this:

While the other (the file with bright colors) shows this:

