I think this diagram from the DeepSeekMoE paper explains it the clearest:
https://i.imgur.com/CRKttob.png The one on the right is how the feed forward layers of DeepSeek V3/R1 work, blue and green are experts, and everything in that right section is what counts as "active parameters".
K (K=8 for these models, but you can customize that if you want) experts of 256 per layer are activated at a time. The 256 comes from the model file, it's just how many they chose to build it with. In these models there is also 1 shared expert which is always active in the layer. The router picks which k routed experts to use each forward pass and then a gating mechanism combines the outputs. If you sum the 1 shared expert + K routed experts + router + output networks you end up with 37 B parameters active for each feed forward layer pass. The individual experts are therefore much smaller than the total (probably something like 4 B parameters each? I've never really checked that directly).
Or, for the short answer: "37 B is the active parameters of 9 experts + 'overhead', not the parameters of a single expert".