Yes, it is a good analogy. And you're correct that this is not chattel slavery.
However this variant of slavery requires that we sell our bodies to whom will buy them. Instead of a lifetime commitment, it's per hour. I will never get back time I sell, and no amount of money can buy back that time. Many places also try to claim the contents of our mind as well as our physical output.
And what happens if we don't engage in selling our bodies? Well, we run our money down. We miss paying bills. We get our car repo'ed. We lose our home. We resort to food banks and soup kitchens and SNAP.
And the result here is you become homeless. Unlike the slaver's whip, this is the eventuality threatened to anyone who can't or refuses to work. And naturally, the existing homeless are used as a threat and a sign to all those who would act out, as a threat to anyone wanting to upset the system.
It also explains why we have homeless in the great quantities we do. It's a trap that you cannot get out of by yourself, and lifting people out removes the societal 'sign' of this threat that it entails.
When I said that you choose your own slaver in this system, I sincerely mean it. I'm required to sell my body on threat of destitution. I just so happen to choose who I sell my body to. (The only people exempt are those born in rich families that needn't sell themselves.)
You have so many choices, including setting up your own business if you don't want to work for others, or living somewhere that is inexpensive and working less.
From my perspective you are just complaining that the universe does not owe you a living.
Slaves had no choice. That is what made them slaves. You do have choice, even if you don't like your current choices.