There are innumerable memorials in the (US) District of Columbia, but I've only seen two monuments - to Washington and to the First Division.

What, if anything, is the difference between a monument and a memorial?

Interesting question. Both words in their etymological senses have something to do with remind, memory: monumentum (fr. L moneo 'to remind') 'that which serves as a monument or memorial;a remembrancer' and memorial (fr. L memorialis 'of or belonging to memory or remembrance; memorial (post-Aug.); (pl) memoirs'). In Latin, it seems that memorials have more to do with writing, and that monuments with structures. Monumental in English also has connotations of large size.

Thus might a monument outlast any remembrance of its memorial function?

I met a traveler from an antique land
Who said: Two vast and trunkless legs of stone
Stand in the desert. Near them, on the sand,
Half sunk, a shattered visage lies, whose frown,
And wrinkled lip, and sneer of cold command,
Tell that its sculptor well those passions read,
Which yet survive, stamped on these lifeless things,
The hand that mocked them, and the heart that fed,
And on the pedestal these words appear:
"My name is Ozymandias, King of Kings:
Look upon my works, ye Mighty, and despair!"
Nothing beside remains. Round the decay
Of that colossal wreck, boundless and bare
The lone and level sands stretch far away.


-Percy Bysshe Shelley
1792-1822

I would say the answer is fairly clear. A monument is a structure which is a memorial, whereas a memorial can be merely a plaque on the wall (as an aside, how did plaque come to be used for teeth as well?)or even just a page in a book, or of course a structure. One of the most impressive monuments in my opinion is the Canadian armed forces one at Vimy Ridge.

I think the consensus sounds right - monument involves large edifice, while memorial is more generally that which "reminds" us.

Perhaps not unexpectedly down in DC, things are reversed.

Both Jefferson and Lincoln "memorials" have monumental statues and only Washington's and one other memorial are labeled "monuments..."