Paragraphs are block level too.
These spans though, they are not block-level. They are inline. You can see how there's a bunch of them all on one line and ... inline with each other.This second set of spans are inside a p tag, but they're not block level either. The p they are in is block level, but the spans are not. You should be able to see a bunch of small boxes inside a big box that goes all the way across. Things like strong are inline too, and so is this link
Block level things are more flexible in terms of positioning. So if you want to spread bits around the page like you described they're probably easier to work with. You can however make inline elements behave like they are block-level with CSS.
These spans are now block-level. You can see that each one starts on a "new line" and goes all the way across the page. This has been achieved with CSS. EGG!