Elnan- if you plates are different widths/lengths - they are for two different machines. IIRC, New Home is the narrowest (and looks almost the same as the National) and Singer/Free (and some Whites made for Sears) take the widest.
I probably have 4-5 Greist style tuckers - they made several modifications over the years. Same with the Ruffler.
Sounds like you have an assortment from different sets - the fun part is figuring them all out!