Thanks. I have to correct myself after some extra study on the results. It is nog the loss which gives different results. I think, but am not sure, that the backward() function might run differently for both groups I talked about before.
I ran the code while printing both version of the loss: 1. torch.mean(torch.square(output - labels)) and using 2. nn.MSELoss(). Every iteration they give the exact same result.
However, when using method 1. in my model to train on, the results (and following losses) differ from those while using method 2. to train on.
Again, in both cases both loss-functions give the same result every iteration:
Using 1. to train on gives a loss of 2.771e-1 (for both methods), my trainable parameter values are R = 1.120 and C = 8.881e-1.
Using 2. to train on gives a loss of 3.639e-1 (for both methods), my trainable parameter values are R =  1.388 and 9.691e-1
My question is, is it expected to get different results while using method 1. instead of 2.? And why is this probably be the case?