I can see the importance of the usage of Federal or Union for some applications but during the time frame of 1861-1865 it meant two different things to two different entities. I cannot see how using the term Federal is in any way making something bigger and better or more powerful than another. Neither is Union. They are interchangeable to me.
After 1865, I do agree on your statement that the term Union made the rest of the world take notice and any little schemes they may have been thinking were not going to fly. After 1865, we were a Union. We remained a Union. Even though it took quite a long time for some from the former Confederate States to adjust to it. A ‘United’ front on the rest of the world was the best weapon we had. We were together for both World Wars, Korea, Viet Nam, the Gulf War, Iraq and Afghanistan.
Until the last couple of years, I never believed it would be challenged from within again but I’m not so sure now. The Central part of the Union has again over run its limits and gone into the states area of control or decision making. In doing so, I believe we are getting a much clearer picture of just why the Confederate States did what was then unthinkable. IF there is a next time, it won’t be as geographically simple.