Thank you for your question, I'm glad you are using the platform so actively.
I just did some research and found an article that explains the different pillars of pension (also private pension) quite well: https://www.expatica.com/de/finance/german-pension-pension-in-germany_831124.html
This is what the website says about private pensions:
"The third pillar of the German pension system is made up of the private pension sector, which incorporate a varying range of individual pension investment plans. These can be set up through banks and insurance providers to increase your total German pension entitlement when you reach pension age.
The main private German pension plans include, but aren’t limited to, the Riester and Rürup plans. These have certain tax and government subsidy benefits, which vary depending on which German private pension you invest in:
- Riester Pension Plan: This is a life annuity plan that requires a minimum of 4 percent of annual income to be paid into the plan, which is then subsidised by the government up to EUR 2,100 per year so suitable for low-income earners. It comes with a choice of five investing variables to suit different circumstances, however, pension benefits are 100 percent taxable.
- Rürup Pension Plan: This is a more flexible life annuity plan better suited to self-employed and freelance workers. It comes with three investing varieties and during the contribution period the contributions are tax deductible. A certain percentage of pension benefits are taxable, however, at around 74 percent (2016) which will rise 2 percentage points annually until 2040."
There is also Mike's answer on this thread:
Maybe it would help contacting the "Deutsche Rentenversicherung" (German pension insurance) and asking them for support. On their website you can search for the nearest location here: https://www.deutsche-rentenversicherung.de/Allgemein/de/Navigation/5_Services/01_kontakt_und_beratung/02_beratung/01_beratung_vor_ort/01_servicezentren_beratungsstellen_node.html
(PLZ means postal code and "Ort" means the city/town you live in)
I hope these sources help to understand the different options a bit better.
Please let me know if you have any other questions.