Moving coil and Moving magnet really the same for my cartridge?

No, because you likely wouldn’t have enough gain.  But without any actual data, even the name of your phono stage, it is impossible to say for sure.  Most likely the low setting of your MC inputs is affording significantly more gain than do the MM inputs, pending further information.

I believe you can if it is a high output moving coil cart.

Dear @markj941: You can use your MM cartridge in the setting positions: MM, 47k and check if your phono stage comes with impedance settings and look wich one is better with your cartridge trhough listen it.

Normally a MM setting has the rigth gain for MM when in the MC position7setting can be settings for different gain.

Regards and enjoy the MUSIC NOT DISTORTIONS,
R.

Raul, Hana SH is a HOMC cartridge. I doubt it has enough voltage output to drive an MM stage, but it might; we need more data for both the cartridge and the phono stage, don't you think?

Yes, but the OP did not give you an answer yet.
R.