I'm curious why you see these 2 things as different.

Situation #1. 2 founders, one investor. 2 founders quit their jobs, have no money in the back. Investor invests $1 million. Money is used to buy equipment, rent office space, play living wages, hire contractors.

Situation #2. 2 founders, one has $1 million, the other has nothing. Money is used similarly.

It seems like the founder contributing $1 million in the 2nd case should get all the same considerations as the investor in the 1st case.

In other words.

    2 founders
    founder #1 1/2
    founder #2 1/2

    2 founders, 1 investor
    founder #1 1/3
    founder #2 1/3
    investor   1/3

which seems like it should lead to

    2 founders only one of which investing

    non-investing founder  1/3
    investing founder      2/3s (1/3 for being a founder, 1/3 for investing)

I know it's not that easy but I can't see any reasonable way to resolve this. The founder who contributes no cash will likely feel like a 2nd class founder because there's no reasonable way they can own half the company. They can agree they both get the same number of shares but then that makes the founder who contributed the money feel like he took all the risk and got nothing for it.

Off the top of my head, one possible way to resolve it might be to let the founder contributing cash to vest quicker. So day one 25% of his shares have vested and he starts vest 2% a month immediately. That means in 3 years he'll have 100% of his shares where as the founder contributing no cash will require 4 years to vest at which point they'll be equal 50/50?

Of course arguably that's still not quite fair to the founder that contributed cash because his deal is not as good as if he was split into 2 people, founder and investor.