I would like to eliminate BOTH the outer border of a terminal window (e.g. the white 1px line around the terminal view) and the inner border (1px or 2px of extra space the term program wastes). The objective is to tightly tile a number of terminal windows into the display.

I will be alternating the background color of each terminal. If I did not, such tightness would make them all look visually like one big terminal. This is all about space squeezing. I have a 1920x1200 display, and a terminal at the desired font size uses 480x400. If I can eliminate every bit of wasted space, I can have a 4x3 grid of these with no borders.

If only monitors added just a few more pixels of space around the edge, I'd have had enough room to to fit the grid in place.

And yes, I do understand that if I make the background color fully transparent, and have no text, I won't be able to see the window at all ... except for the title bar which I would also like to remove (and have all the functions moved over to a right click thing).

It depends on your window manager.

Is this you are looking for?
https://bbs.archlinux.org/viewtopic.php?id=104868

Might be. But I don't know how to make the terminal program(s) do that in the systems I run (Slackware with Xfce, Ubuntu, and Xubuntu). I suppose if there is a generalized way to do it for any app, that would be good. Better if I can somehow tag an app when I start it, so that one instance of an app will have this applied to it because I tagged it a certain way, whereas another instance of the very same app not so because I tagged it a different way (or not at all).

I think it belongs to the window and the content (what is running inside) is irrelevant. You need to start a window which has the capability to set what you need.
So you can try to download and run urxvt (package name: rxvt-unicode), there is an option -bl to set it borderless.

If you want an app to use this urxvt you may need to create a launcher to do that (urxvt -bl [options] -e your_app)
If you have an app with its own graphical features (so it draws its frame) you would need to implement the borderless feature and build into the app.