Both RTD and Reentry are the same document and cost the same money.You may apply for RTD or a Reentry Permit.But the difference is RTD is valid for 1 year and allows you to go to Germany without visa .In your RTD it's marked Refugee Travel Document above your Photo and the category is asylee(or refugee if you are).If you are a Permanent resident as a result of asylum(This is your case) or refugee,the category will be Permanent resident.The permit is valid for 2 year and above your photo,it's marked Reentry Permit.You nee a visa to go to germany with a reentry Permit.I will advise you to apply for a Permit because there is no refugee word somewhere and it's good for 2 years.As a US PR,getting a visa from any consulate is not a big deal.If you don't hear about the word visa,apply for RTD and go to Europe without a visa via Germany.About,the card,mine is backdated Sep 15,2004 and expire on Sep 15,2015.This means,your are resident since 2004,but the card is issued in 2005.Then,2005-2015 makes 10 years.Forget about the year 2004.It comes like they issued one to you in 2004 valide for 1 year,and in 2005,they renewed it now for 10 years.This means,if you don't apply for citizenship,in 2016,you're gonna get another one which is gonna expire in 2026.But in that card,they will mark,residence since 2004.It's gonna be like your card is for 22 years.
Enjoy your freedom man.