shooting line can be many things. you can cut the head off of a regular line and use that, you can buy "shooting line", you can use mono. All have strengths and weaknesses.
Using the running line from a "normal" is nice because it is generally thicker and easier handle than shooting line. It wont usually cast as far though and takes up more room on spool. Shooting line is thinner and casts further, but the thinness can be problematic. Mono is cheaper and can be good but is prone to tangling etc. FWIW I have never spey cast but use shooting head systems for salt, which is why I didn't comment on the effects on casting styles etc.