I assume these are 401k plans.

Pre-tax (Standard): Pay taxes on your contributions upon withdrawal. This lowers your current taxable income, which may be beneficial.

Roth: Pay taxes on your contributions now. Gets taxes out of the way (no one knows what future tax brackets may be), especially good if you start your career in a lower tax bracket. For most high-earners, a Roth 401k is usually not a good idea.

After-tax: This is a standard 401k but you can add additional money (already taxed like in a Roth) above the standard contribution limit ($22,500 for 2023 and if <50) to a max of $66k (including employer match) in 2023 if <50. However, earning are taxed, and is the only plan where this is so.

Now sure why the standard Pre-Tax and After-Tax are both offered (After-Tax is the same if you don’t contribute over $22,500 from paycheck deductions). Only thing I can think of is that the funds/investments offered are different.

General advice is to either invest in index funds (S&P 500, Total US Market, Total Foreign Market, Total World Market) or invest into Target Date Funds (you select the one with a date closest to your retirement date and it handles the allocation of investments for you and changes every year, doing more stocks at the start and more bonds towards the end). And make sure the expense ratios (fees) are low, below 1% for sure but below 0.25% even more so.