That China means "from China" was pretty simple, much more interesting is from what porcelain came out:
Look up porcelain at Dictionary.com
1530s, from M.Fr. porcelaine, from It. porcellana "porcelain" (13c.),
lit. "cowrie shell," the chinaware so
called from resemblance to the shiny
surface of the shells. The shell's
name in Italian is from porcella
"young sow," fem. of L. porcellus
"young pig," dim. of porculus
"piglet," dim. of porcus "pig."
So we have a shell (cowrie) that resemble a young sow. Then came this new material from China that resemble the shell material for smoothness and glossy, so they took the Italian name of the shell for the material.
Curiously enough now the shell is called Ciprea in Italian, I never heard the word Porcellana in Italian in relation to any shell.
Nothing really. In English you tend to get a lot of words that mean the same thing, sometimes there are historical or poetic reasons for choosing one word — but not in this case.
Other than big being a much more common word and large sounding more refined there aren't many areas where you would use one over the other for purely grammatical reasons.
Note that big can also mean "major or important" — so big decision, big spender.