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According to these sources Germanys waste US waste, Germany produces 411 million tons of waste in the year 2016, the US about 260 million US tons.

Is it true that a country with smaller GDP and a quarter of the population produces so much more waste? Does the US not classify certain kinds as waste?

The reason for this discrepancy is because the data from the Umweltbundesamt includes construction and demolition waste (see figure below and surrounding text on your linked webpage) whereas the data from the EPA "does not include everything that is landfilled in MSW, or nonhazardous, landfills, such as construction and demolition (C&D) debris, municipal wastewater sludge, and other non-hazardous industrial wastes." The EPA data you cited only includes "trash, or municipal solid waste (MSW), as various items consumers throw away after they are used."

If you are interested in data for just municipal solid waste (like in the EPA website), @Milster has recommended this Statista page where it is shown that Germany has produced 51.05 million metric tons of MSW in 2017 whereas the Unites States has produced 258 million metric tons. Thus, the US produced 5 times as much municipal solid waste as Germany in 2017. The Statista values for US MSW in 2017 approximately agree with the EPA figure (below).