Patch (apply) vs. Pull

In trying to understand git I've adopted a mental model where everybody
duplicates locally the remote history in which they are interested.
These histories have various points in common, allowing for intelligent
merging. That makes perfect sense to me, until I look at the list
archives filled with patches.

How exactly are these patches being generated? Is there a right-way(tm)
which causes the recipient's a later pullers' histories to be
intelligently handled in the future?

TIA.

--
Darrin