As a general rule, students also have to make social security contributions (health, long-term care and pension insurances) and pay taxes if their income is above a certain level- so depending on your income, it may be that you have to pay both (social insurances and taxes), only one of the two or neither of them. Here the scope of work and your income are the main determinants. If you earn less than 450 euros per month -including additional revenues such as Christmas bonus ("Weinachtsgeld") or holiday pay ("Urlaubsgeld")-, it means you have a so-called "Mini-job" and do not have to make any social security contributions or pay taxes. If you earn less than € 450 per month, you may also be covered by your parent's or spouse's insurance scheme, provided the remaining requirements are met. You can find out more about family insurance on studis-online.de.
If you earn between 450.01 euros and 850 euros per month (or have a so-called "midi job"), in principle, you can no longer be covered by family insurance and have to join a health insurance scheme independently. In principle, students can join a statutory health insurance scheme using affordable student tariffs. You can read more in this regard on studis-online.de.
You also have to make pension insurance contributions, but you only need to pay for unemployment- and long-term care insurance if you work more than 20 hours a week. That means if you work less than 20 hours per week, you are exempt from contributing to unemployment- and long-term care insurance. When you have a midi job, however, you have to pay taxes: Your employer will automatically deduct your taxes from your salary and pass them on to the Tax Office. To do so, your employer needs your tax ID ("Steuer-ID"). The deducted amount, however, will be paid back to you after your tax return next year, if you earn less than the tax-exempt income level during the year. You can find out more about the current tax deductions on mehrwertsteuerrechner.de. In any case, doing your tax return is worth it, as you can deduct professional expenses or training costs and win some money back.
If you earn more than 851 euros per month, you will lose all student privileges and have to make social security contributions and pay taxes like a regular employee.