What is it?!
They are technically different; In general terms, a chest of drawers is narrow and tall while the dresser is low and long. Dressers generally have 5 or more drawers that are deeper and wider than a chest of drawers and are more likely to come with a mirror mounted. They're more specific to bedroom storage, where a chest of drawers can be used through out the home as storage for all and sundry.
Though, going back to the bedroom, a chest of drawers is better suited for a smaller bedroom while the dresser is great when there's more floor space and of course, if space isn't an issue - why not get a matching set for the cohesive look.
Above and beyond all that...
You have the Double Dresser; which as the name indicates is made up of two (maybe more) columns of wide drawers - this needs a LOT of space, so as not to overwhelm a room - great for setting a television on, among many, many other items.
Or the Standard Dresser; One column with two or more rows of long wide drawers, not as wide as the double dresser but still plenty of room for the TV or use it as an oversize bedside.
What about a Combo Dresser; made up of a combination of drawers and wardrobe; sometimes with hanging space and sometimes with shelves - ideal for the odd shaped items we all struggle to store - hats, handbags, shoes, scarves etc...
Would you prefer...
A Standard Chest of Drawers? This small bedroom staple is taller and more narrow than it's long, low brother but equally functional. It does have more rows of drawers, but they tend to be shallower than the dresser drawers.
Not enough room for all your smalls? What about a Lingerie Chest? Thinner and taller than your standard chest of drawers, this can also be used to store other compact items, makeup, jewellery etc... Maybe use it to store seasonal clothing, i.e. swimmers.
Would a Gentleman's chest be a better storage solution for you? Similar to the Combo dresser with a combination of drawers and wardrobe, this is quite a versatile piece, with the added advantage of being taller and wider than the Combo dresser.
So?! What will it be...?