I understand the exact difference will vary from bank to bank. But in general, I understand that savings accounts have a higher interest than checking. So if it's that simple why not always use the savings account and put all the money into it? I'm guessing there's other restrictions like how often you can make withdraws/deposits from a savings account. Is a tax free savings account just a specific type of savings account? From what I read checks can only be made from checking account but I never pay by check.
(This is a Canadian-focused answer and comments from Americans about how it's different there are not needed, thanks.)
Once upon a time, there was a huge difference. Only with a chequing account could you be out and about, nowhere near a bank, and pay people for stuff from your account (by writing them a cheque.) But now we have debit, and you can totally pay people by debit from your savings account. It's a choice.
One big driver of the choice is service fees. For example, your savings account may pay you some piddly interest, and then charge you $1 for each withdrawal. Your chequing account won't pay interest, but might give you 30, or even unlimited, free withdrawals a month.
For example, ScotiaBank (which doesn't seem to call accounts chequing any more, though some are called saving) has a table of fees. Comparing these is the way you would choose the account that works for you.
It's also possible that your chequing account has overdraft protection that might let your automatic payments still happen even if you don't have quite enough money in the account, or let you withdraw more than you have at an ATM. This would vary branch by branch, and you probably shouldn't rely on it, but it's another difference: savings accounts would never have overdrafts.