The moss looks like Leptodictyum riparium from populations growing in waters in Germany and looking different to the well known "Stringy moss".
A moss looking like this is sold in Germany under the name "Drepanocladus sp. aduncus". But it has nothing to do with the real Drepanocladus aduncus.
The leaves of L. riparium have a distinct midrib that doesn't reach the leaf tip.
Leaves of Fontinalis ("willow m.") are arranged in 3 distinct rows along the stem, and lack a midrib (but are often folded in the middle).
For comparison, pics of wild growing Leptodictyum riparium, a common water moss in Germany (not the Stringy moss! I don't know if Stringy m. is correctly identified as L. riparium). I've ID it using a moss flora (Frahm & Frey).
From the river Leine, Germany, You can see the midrib in some of the leaves:
the midrib is the thicker stripe in a single moss leaf. It's better visible with a magnifier. OK, hardly visible in my pics...
Some mosses lack a midrib or have 2 short ribs in the base of the leaf, e.g. Java moss.
Leptodictyum riparium is widespread and frequent in the northern hemisphere and very variable but there are some other Leptodictyum species and I don't know how they differ. There are also more similar genera, e.g. Amblystegium (Leptodictyum is counted among Amblystegium by some authors, too).
Can you describe the growth patterns of the L. riparium that you have? Mine tend to grow horizontal (not vertical like the better know stringy moss) with a lot of branching similar to that of christmas moss. Is this growth typical of this moss?
my Leptodictyum riparium has the same growth pattern! It grows horizontal too, and the branching seems to depend on the lighting. In my tank it was sparsely branched, but outdoors it is often intensively branched (see my last photo). In the nature it creeps often on stone or wood.
I have no idea what species the upright growing "stringy moss" really belongs to. E.g. Drepanocladus aduncus has a similar growth pattern, but different leaves.