"If you bought medical insurance policies on your own for yourself or your family, you might qualify for a self-employment tax deduction on the premiums." [1]

"If you are enrolled in an employer-sponsored health insurance plan, your premiums may already be tax-free. If your premiums are made through a payroll deduction plan, they are likely made with pre-tax dollars, so you would not be allowed to claim a year-end tax deduction." [2]

[1]: https://www.nerdwallet.com/article/taxes/self-employment-tax... [2]: https://www.investopedia.com/are-health-insurance-premiums-t...

I'm confused. What's the difference between a "tax deduction" and paying with "pre-tax dollars"?

Do they mean if for example a company pays $5000/year in employee insurance, they can subtract $5000 from their tax bill? If so, that's a tax credit right?

As I understand it, a "tax deduction" is a deduction on taxable income (in the case of an individual) or profit (in the case of a company).

You are right, pre-tax dollars is the same as tax deduction. But for self-employment (the first point), there are more conditions, and people might be out of luck. For example if you could be insured by your spouse's employee based insurance, and you choose to buy your own insurance.