After-tax 401(k) contributions are employee contributions made with money that has already been taxed, into a separate account inside the plan, and they are a different animal from the two contribution types most people know — the pre-tax deferral and the Roth 401(k). The name causes genuine confusion, because a designated Roth contribution is also made with after-tax dollars — so "after-tax contributions" sounds like a category that includes Roth. It does not. In plan terminology these are non-Roth after-tax contributions, tracked separately from both pre-tax deferrals and Roth deferrals, and they are also distinct from a nondeductible traditional IRA contribution, which is a different regime reported on Form 8606 that happens to share the phrase.
The mechanical difference from Roth is one sentence long and it is the whole point of the page: your contributions become basis you eventually recover tax-free, but the earnings on them remain pre-tax and are taxed as ordinary income when they come out. A Roth contribution, by contrast, makes both the contribution and its growth tax-free in a qualified distribution. So after-tax contributions left sitting in the plan for decades produce the worst of both worlds — no deduction on the way in, and taxable growth on the way out. Their value comes almost entirely from being converted to Roth, promptly.