Presidential and congressional terms don't start/end the same day

[Sir Mohamed]

I always wondered why the presidential and congressional terms do not begin or end on the exact same day. Congress constitutes on January 3, while the president takes office on January 20. What's the purpose for it?

A theory: That the new congress elects the president and vice president in the case of a EC deadlock? But before 1933, both terms begun/ended on March 4.
And it's the same in some states: Here in California, the terms for state lawmakers begin in December, while the governor is sworn in January. Why isn't it the same date?

[Sir Mohamed]

Also, in theory, an incoming president could submit his cabinet and other high level officers to the Senate for confirmation so that they could take office when he does, tho I don't think that's ever happened.

Sounds reasonable. And the same in the states?

It's interesting because an old chief executive (prez or gov), who is defeated for reelection but whose party maintained a majority, could sign controversal bills of the new legislature into law.

That happend in the 2014 midterms in IL (Dem. Gov. Quinn defeated but Dems maintained majority) and PA (GOP Gov. Corbett defeated, but GOP increased (sic!) majority).