Taught & Taut

With the gh – (v.) past tense of Teach.
Without the gh – (adj.) stretched tightly.
As in, "I just taught you what taut means."

Moan & Mown

As in, "You can complain all you want, but you still have to cut the grass. Now get out there."
–my dad, circa 1993.
–my wife, circa 2003.
–me, circa 2013.

Shone & Shown

-one – past tense of Shine.
-own – past tense of Show.

Albumen & Albumin

-en – Yes, egg whites actually have a name.
-in – a protein found in, among other things, egg whites.
I'm sure this will come in very handy in your day-to-day writing...