A 401(a) is similar to a 401(k), in that any contributions you make are excluded from your taxable income. You will pay tax on the money when you withdraw it in retirement, and if you withdraw funds before age 59-1/2, you will also pay a 10% penalty. Also like a 401(k), you can only contribute by payroll deduction, you can't make cash contributions from your bank account. You may be able to rollover tax-exempt retirement funds from an IRA or previous employer into a 401(a) at your current employer, but that depends on their rules.
The main differences are that a 401(a) plan is used by government and other public employers, while 401(k) are used by for-profit corporations and 403(b) accounts are used by educational institutions and non-profits. Participation in a 401(a) is often mandatory.
Also, you may have higher contribution limits. The maximum contribution to a 401(a) plan is $66,000, including employee and employer shares. But a qualifying employer is allowed to offer both a 401(a) and a 403(b), and the contribution limit for a 403(b) is $22,500. So if you work for a government employer that offers a 401(a) and a 403(b), you can contribute substantially more than someone who only has a 401(k) or 403(b).
For example, I work at a government university. I am required to participate in the 401(a) with a mandatory 5% pre-tax contribution, that is matched by the employer. I can't contribute more. But they also offer a 403(b) so if I want to contribute more than the mandatory amount, that extra contribution goes into the 403(b).
