Anecdotally, I’ve noticed that this distinction is starting to get lost or muddled. I can’t give you specific examples, although there is a furniture shop close to where I live with the rather wonderful advert for “chester draws” (I do try not to mock odd use of English, but I rather like the inventiveness of this one, hence sharing it here).
To draw (a verb) is to make marks on paper with a pencil, or on another material with another medium, in order to produce a picture. It also means to drag something along or across (a horse draws a cart, we draw the curtains when we close (or open!) them); to reach a certain point (“we hope that the meeting will draw to an end by 7pm”); to work out (you draw conclusions); to attract attention (“his miming act drew a smaller crowd than he’d expected”) and various other technical things to do with pipes and sails and water.
There is a noun, draw, but this means a process by which a winner of something is selected randomly. (“We will have a draw of the raffle tickets at the end of the fete”), a game that ends in the same score for both sides or, in cricket, where the match has to be abandoned because it can’t be completed in the time allowed (“The match was a draw. Both teams got 1 goal”), or an attraction (“her burlesque act was a big draw and the variety show made a huge profit”). What it isn’t is anything to do with furniture.
A drawer (a noun) is the slide-out compartment in a piece of furniture, kitchen unit, desk, etc. It’s also a rather old-fashioned word for underpants, a drawer is someone who draws something, and you can be the drawer of a cheque when you write one. But the main use is the one to do with furniture.
“The winner of the prize draw received a beautiful chest of drawers. I’m going to draw a picture of it for the person who donated it, so they can remember it.”
You can find more troublesome pairs here and the index to them all so far is here.
LibroEditing proofreading, editing, transcription, localisation 
Madeleine
March 17, 2014 at 4:06 pm
Being Canadian, with a UK Dad, there are some interesting pronunciations around the dinner table. When he said “DRAW”, as in “I am going to draw a picture”, it sounded like DRAWER, as in where you put your clothes. Same with the name Laura. We thought it sounded like LAUR-ER when he said it. ‘Not sure which areas of the UK speak like this…his mom and dad were from two different parts of England. Anyway…vive la difference…’makes the world go ’round!
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Liz at Libro
March 17, 2014 at 4:07 pm
It does, and as long as people know the difference and which one to use when they’re writing it down, that’s all I need …
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Kristen
June 10, 2014 at 8:52 pm
Just a small correction! You wrote “There is a noun, draw, but this means to select a winner randomly […].” Technically, you defined a noun as a verb and then used it as a noun in the sentence that followed in parentheses. To select a winner randomly is the verb to draw; the selection of a random winner, the draw, is the noun. Just a minor quibble, but I knew what you meant of course!
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Liz at Libro
June 11, 2014 at 12:02 am
You are of course correct and I will amend the post when I have a moment – thank you!
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Bob
February 11, 2016 at 9:03 pm
You can also draw money from your bank account, water from a well or draw out the drawer! If you make something last or be longer you can be said to draw it out. Language like life, is complicated.
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Sir Loin, of Beef
March 7, 2018 at 2:29 pm
After checking the Oxford dictionary, I see that one definition of “draw” refers to making a single selection from a group of possible candidates at random. However, I have never seen this used anywhere but online discussions regarding the word “drawer” being incorrectly spelled “draw”.
Everything I’ve ever read has called it a “drawing”, since “to draw a ticket” for example, uses the word as a verb.
People that spell drawer without the last two letters are simply ignorant of the correct way to spell the word. The two are not interchangeable.
Often mentioned is a supposed definition describing a person who engages in the act of drawing something (with a pen, pencil, etc.), such as a portrait or technical drawing, which has also come to be considered correct by many.
In reality, this is not the case (or was not in the past). There are other words to describe one who draws: illustrator and draftsman. Others words are more specific, and their definition would be described by these two.
Finally, although the recipient of a check may be called a “drawee”, the depositor writing the check is known as the “maker” of said check.
I assume these somehow forgotten words exist at least in some form to distinguish them from the word “drawer”. It certainly makes more sense than the dubious, or seemingly contrived ways some people use it in a sentence.
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Liz Dexter
March 7, 2018 at 2:43 pm
I think your “single selection from a group of possible candidates” example is what I’m talking about when I describe a “prize draw”. I do certainly see this used in advertisements for … well, prize draws, etc. I try to go with what the correct examples are rather than the ways people go wrong; I’m not sure whether you’re describing my own example sentences as contrived, but of course they are, to fit the topic! I can assure you that I consult a range of dictionaries and other sources while writing these articles.
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