This confuses a lot of people and even I get spooked by it some times. What I’m guessing is happening, is that your currently open project 01.TBTH.Intro in that screen shot was actually created in the Library 2017_03.14b.Library_MickTBTH. You are now pulling files from the new Library 2017_03.26_NEW.Library_MickTBTH into the old project and since every Library is really a self contained folder on the file system, FCP X is telling you that it will need to copy the clips between the two Libraries so that the Library remains self contained, unless you have elected to leave files on the filesystem.
I see that you have Libraries called “xxx_Library”. I would forget that it is a Library and think more about what it really represents in the real world to you. I don’t know your workflow but please allow me to share my workflow with you so that you can see how I use Libraries. This is just my workflow and may not be appropriate for your work but it serves as one example use.
I do work for clients on an annual basis. I create one Library per client. For example: I do work for Boris FX creating training for Boris TV. I create one Library called Boris TV where all of my work for the year is done. I create one Event for each episode. So I have Events like 01-3D Text Basics, 02-Animating Text, 03-3D Extruded EPS-1, etc. Each Event has 3 Projects. One is the finished demo to show at the beginning of the show. The second is the demo that I build during the show, and the third Project is the show itself (i.e., my recorded demonstration). All of the media for that episode is imported into that Event. That keeps each episode and all of it’s media under one Event which is named for the episode. Sometimes episodes share media but that’s OK because everything is under one Library for that client. At the end of the year, I usually start a new Library just so that the Libraries don’t get too big. I keep all of my media in the Library so archiving everything is as simple as just dragging and dropping the Library onto an external hard drive. This is what one of my Boris TV Libraries looks like in FCP X:

This approach might not make sense for your work. Some people mix multiple clients projects in a single Library because that’s what makes sense for them. If your project is a documentary, you might want one Library that is the documentary and the Events are days of shooting or locations and then another Event that contains the projects (timelines), etc. It’s all up to how you want to use it but you have this hierarchy of Library -> Events -> Projects to logically partition your work. Use that hierarchy to your best advantage.
I’m not sure what mistake you thought you made that caused you to create a new Library (I might have just deleted the Event that I imported media under and created a new one) but perhaps if you discuss it further here, we can guide you as to how you could have corrected it without having to start over with a new Library and now get confused by having two Libraries with media being copied between them.
Getting back to your question about what’s going on… I’m pretty sure that your Project lives in the other Library. What I would do is close the other Library (right-click the name and select Close Library) and just work with the new one open. This should elevate any confusion about where your media is coming from. Hope that helps.
BTW: Here are some links to those Boris TV training episodes if you are curious: ???? #ShamelessPlug
Extruded Text Basics in FCP X, Part I & II
https://borisfx.com/videos/extruded-text-basics-in-fcp-x-part-i/
https://borisfx.com/videos/extruded-text-basics-in-fcp-x-part-ii/
Extruded EPS Basics in FCP X, Part I & II
https://borisfx.com/videos/extruded-eps-basics-in-fcp-x-part-i/
https://borisfx.com/videos/extruded-eps-basics-in-fcp-x-part-ii/
Up Rez in FCP X & Motion 5
https://borisfx.com/videos/up-rez-in-fcp-x-motion-5/
Custom Presets in FCP X Using Motion 5
https://borisfx.com/videos/custom-presets-in-fcp-x-using-motion-5/
Type On Text in FCP X
https://borisfx.com/videos/type-on-text-in-fcp-x/
Corner Pinning in FCP X
https://borisfx.com/videos/corner-pinning-in-fcp-x/
BCC Beauty Studio: Skin Retouching
https://borisfx.com/videos/bcc-beauty-studio-skin-retouching-plug-in-for-fcp-x/
~jr
http://www.johnrofrano.com
http://www.vasstsoftware.com