What is the difference between a ¶ Pilcrow Sign and the § Section Sign?

Usually, the pilcrow is used to indicate paragraphs, not only when citing them: you can use it to indicate the paragraphs' beginning or end, or to separate them if you are writing them without breaks. It can also be used if you have run out of symbols to indicate footnotes in a given page (the order of footnote symbols is traditionally *, †, ‡, §, |, ¶ in English). The section sign is much more usually employed in citations, and can indicate paragraphs, sections or footnotes. I'd say the use you mention is correct, as long as what the sign is pointing to is clear.
There's a fine text on the pilcrow and its history in Shady Characters: The Secret Life of Punctuation, Symbols and Other Typographical Marks by Keith Houston, a book which, oddly, devotes less than a line to the section mark.

The pilcrow (¶) was traditionally genuinely used to mark the start of a new paragraph - or, perhaps more specifically, a new idea or section. It was used before the convention of leaving a clear line, or dropping a line and indenting the first word, came about, but it served more or less the same purpose. It was used, for example, in the King James Bible - which, of course, is separated into verses. Since each verse begins on a new line, the pilcrow is actually very useful here for marking out paragraphs. See:

Genesis 1

Here they actually look like double struck 'C's.

This is why Microsoft Word uses it to mark out paragraphs.

The section sign (§) had no such office.

(Source (including some very pretty Latin))

I presume that most people refer to ¶ as a "paragraph symbol" because that is what MS Word tells them it is.

If you show paragraph marks and other hidden formatting symbols in Word, (in Word 2013, Home > Paragraph > Show/Hide Editing Marks) you'll see the Pilcrow sign delimiting all of the document's paragraphs.

JMVanPelt's answer says the section can mean paragraph, and that makes sense to me.

In my mind's eye I can see examples of numbered sections one paragraph long. A google search for the section symbol produces mostly legal writings, and I've pored over legal journals and codes of law in school--I think I've seen many instances where one section is one paragraph long. Perhaps a similar grounding in legal writing becomes an unconscious Symbol = Para notion.