EDIT: maybe if my savings account paid meaningful interest I'd use it more, but most retail banks these days don't.
Most of my savings are for short-term things currently (tuition mostly) and so it sits in a savings account with one of the higher APY banks (Ally, Alliant credit Union, and the like). However, when it's money I wouldn't have to pay back somewhere soon, it would definitely go to index funds.
Savings accounts are essentially restricted checking accounts, so what's the point? The interest rates on both types are the same, at approximately zero (pennies of annual interest on a thousand dollars).
Zero risk, but higher returns than a checking account. You may not care about the difference between 0% interest and 1.5%, but it is nice to have a few hundred $$ extra at the end of teh year.
Not sure why banks make any sort of distinction anymore.
I have a savings account at Marcus and it's 1.7% without any minimum, a high $1M max and no goofy rules to jump through.