Along with the difference between a solid state relay and a transistor, I'm also interested to know if there are transistors that act a lot like the typical relay modules you can find on ebay (where you only need a 5V signal from the microcontroller to toggle the state of the transistor...) A lot of transistor datasheets I've seen so far have wildly different saturation specifications (where the collector/emitter value is highly influenced by how much voltage is applied to the base), but this saturation idea doesn't really apply to a electromechanical relay...
https://www.fairchildsemi.com/datasheets/2N/2N3906.pdf https://www.fairchildsemi.com/datasheets/TI/TIP31A.pdf
Doing a search on Digikey's website for solid state relay gave me a list of components that all have input voltages close to 1.25 V... Am I correct in believing the solid state relay is a lot like what I just described?