Are there different minimum wages for different industries?
Yes. There are industries in which a higher minimum wage applies than the general minimum wage. This minimum wage for an industry is stipulated in generally binding collective agreements. A list of specific industry minimum wages is available here: http://www.dgb.de/schwerpunkt/mindestlohn/hintergrund/branchenmindestloehne
A higher minimum wage therefore applies to people working in these industries. It is best to contact an advice centre if you are unsure which minimum wage applies to you.