Using Skype to converse via HDMI & TV

This is long and convoluted but I am trying to be clear ----I was running a test of a Skype connection and something odd happened that I can't explain and doesn't seem logical and I thought I would ask here.

I was testing Skype so I could host a virtual meeting with someone calling in using Skype and we'd project it on the wall and all would be fine. Last time we did this it was fine = made connection, the video/image of the person & audio projected [using an older but working projector connected to my MacBookPro] and we just projected it on a wall and held a discussion just fine.

Now, we were trying to set up essentially the same thing = Skype call, coming to my MBP and then being projected == we can do that fine but we thought we would try HDMI and connect and project via HDMI & a TV. We connected HDMI cable from MBP to TV and while I could see the person skyping with me on my MBP screen, the TV only had an image of the HighSierra screen - and when I went to open SystemPreferences on my MBP it did not open on my MBP but did open on the TV...but no image of me or the other person ever made it to the TV - she and I could see and converse on my MBP [and her computer] - even tho the TV and the MBP were directly connected via HDMi the only thing that showed up was the HighSierra image [the mountains in winter?] and when I opened System Pref. on my MBP it did not open on the MBP but did open on the TV, with the HighSierra image in the background.

BUT then I connected the projector to the MBP - ran cable from it to the Thunderbird port of the MBP and the USB port [using that little connector that allows connecting from WIN port on projector to a Mac], I could see my friend on Skype on my MBP but not the computer nor the projection on the wall. BUT if I took the cables and ran them from the projector to the MBP then the image of my friend ended up on the TV as desired, but when I unplugged the Thunderbolt cable from the computer, it stopped. And this is true whether the projector was on or off.

So, in essence. The MBP is connected directly via HDMI to the TV. There is no image from my friend on Skype on the TV - she is on the MBP just fine. BUT when I plug the connection [Thunderbolt] from the projector to the MBP, even if it is off, the friend shows up on the TV [and the MBP] - If I unplug the connection between the projector to the MBP she is no longer on the TV tho is on the MBP. So, even tho the projector is not running somehow the connection of it to the MBP causes the image from Skype to show up on the TV.