Planting seeds straight into fertilizer?

Hi, I'm using fox farm ocean forrest organic potting soil. I also heard that mixing ocean forrest and regular fox farm potting mix together would be much better. Is potting mix, potting soil and fertilizer the same thing? I'm full of questions but my main question right now is my seedlings. Once they sprout and are ready to put into a growing medium can I put it into mouth wash cups with the ocean forrest soil or should I use a peat pellet and plant it into the potting mix later? I heard puting seedlings straight into soil with fertilizer and nutrients can hurt the seedling since they are weak. Also for flowering I'm going to use an earth box. Is this kind of soil ok for that? thanks!