You should keep in mind, that HTML is intended to DESCRIBE the content it contains.
So, if you wish to convey a paragraph, then do so.
Your comparison isn’t exactly right, though. The more direct comparison would be
When to use a
<div>instead of a<p>?
as both are block level elements.
A <span> is inline, much like an anchor (<a>), <strong>, emphasis (<em>), etc., so bear in mind that by it’s default nature in both html and in natural writing, that a paragraph will cause a break before and after itself, like a <div>.
Sometimes, when styling things — inline things — a <span> is great to give you something to “hook” the css to, but it is otherwise an empty tag devoid of semantic or stylistic meaning.