In the Wikipedia's Quantum channel article, it is said that a purely quantum channel $\phi$ (it's not exactly the same phi calligraphy but it's close), in the Schrodinger picture, is a linear map between density matrices acting on two Hilbert spaces. Then properties of this mapping are given and we find the following notation :
$$I_n \otimes \Phi$$ We find again this difference of notation in the Heisenberg picture paragraph. However I believe $\phi$ and $\Phi$ are the same and I don't understand the change of notation between the twos. Is there a difference justifying this change or is it a lack of coherence of the notation ?