<pre> is for preformatted text such that whitespace characters in it including tabs are preserved, whereas it's collapsed/whitespace-normalized at other places. <code> is for semantically denoting a span or block as "programming language code", which might or might not have whitespace characters preserved. You typically use <code><pre>...</pre></code> for a code block, and just <code>...</code> for an inline code span.

Edit: props for citing the actual HTML 4.01 SGML DTD!