Before Roth accounts were allowed inside 401(k)s there were post-tax contributions that could be made. They served two purposes: You could go above the annual pre-tax limit; You could pull those contributions out under some conditions. Back in the days when you had to turn in the paperwork a month before the last day of the quarter, and could only contribute in integer percentages; if you were coming close to the maximum contribution, being able to go over the limit by having the company treat the excess as post-tax contributions was a big deal.
After the Roth IRA was created there was pressure to allow Roth inside a 401(k). Roth is better than post-tax contributions because the growth in the Roth is tax free.
But if you want to maximize the 401(k) being able to contribute post-tax money is still a thing. The money exists in a middle ground between traditional and Roth. Some plans allow you to make the mega-backdoor conversion to Roth.
Most sites discuss the maximum limit for 2022 as:
Employee 401(k) contributions for 2022 will top off at $20,500—a
$1,000 increase from the $19,500 cap for 2021 and 2020—the IRS
announced on Nov. 4. Plan participants age 50 or older next year can
contribute an additional $6,500, unchanged from 2021.
but skip this part:
The limit on total employer-plus-employee contributions to defined
contribution plans will increase to $61,000 in 2022, up by $3,000 from
$58,000 in 2021.
That means your contributions in traditional plus Roth is limited to $20,500 (assuming under age 50), but the post-tax and employer match can bring the total to $61,000. Even more if you are over age 50.
What’s the tax treatment for after-tax contribution vs. the usual
contribution (i.e., the limit for tax deferred)
When calculating your paycheck each pay period the post-tax and Roth contributions don't reduce your taxable income. The traditional contributions do reduce your taxable income.
If you don't convert them to Roth 401(k) funds then you will be paing taxes on the growth.
Would the money be put in the existing Roth 401k or some other type of
account?
The statements should make clear which funds are which. If you have all three types of funds that should be noted clearly.