Because I know you can draw cheques from a savings account, so what gives?
As far as I can recall, savings and chequing accounts exist due to regulations on the banking industry that put were into effect after the depression to prevent a "run" on the bank.
A chequing account is a "demand" account, meaning you can go and demand your money, and they have to pay immediately, by means of a withdrawal or a cheque. Banks used to get out of hand and loan out pretty much all the money they had on deposit, and of course those people with loans just put the money they borrowed into another chequing account and the bank loaned that out to someone else. The money that people believed they had access to multiplied indefinitely. However, when everyone goes to take that money out at the same time, you have a run on the bank. Therefore, government regulations stipulate a % that the bank must have on-hand. The typical number is 5%. That effectively limits the money multiplier to 19 times.
Savings accounts get around this restriction by putting limits on how much and how quickly you can withdraw the amounts. They pay you more interest because the money in a savings account is worth more to them, because it's not subject to those restrictions.
Some chequing accounts pay interest, but you have to maintain a minimum balance. Some savings accounts allow you to write cheques, but I assume the withdrawal limitations probably still apply.
There's also something to do with deposit insurance (as in, the chequing accounts are covered by government deposit insurance, but savings accounts are not). I'm not 100% certain of that though.
There is very little difference these days between account types.
The fee structure and interest paid is different, but the actual mechanics, and as noted by others, the coverage by deposit insurance is identical.
So look at how much money you have in the account(s) you have; are you maximizing the interest that you could be receiving, even from the small amounts that the banks will pay?
If you could get more interest from the savings account, and only write one or two cheques per month, you might be better off with that account only; but given common fee structures, you likely would not want that as your primary account.
Another reason for separate accounts is more psychological. You might be able to train yourself to not dip in to your savings if you don't have a chequebook.