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

I'm using a Hana SH cartridge and enjoying my vinyl once again. The best setting for this cartridge in my phono preamp is 47k set to MC and using the low output. Does this mean, that I could in fact plug my turntable in the MM inputs with the same settings?
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.
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,
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?
@markj941 why don't you just plug it into MM input to check it out, no harm for your cartridge or phono stage. I have a few High Output cartridges made by the same company who made Hanna, but mine made in the mid 80s. They can be plugged into MM phono stage, no problem with gain, but i prefer MC input with automatic impedance load on my WLM Phonata Reference phono stage with suts inside. It's lound, but with my low power tube amp it's fine, better than 47k MM input.  

HOMC means much more wire for the coils while reduction of

mass by moving parts by MC carts is conditio sine qua non for

the fast reaction of the moving parts: stylus/cantilever combo +

coils. Obviously (?) HOMC carts are made to be used with MM

phono-pres. This means the same as production of carts for

which one does not need an (expensive) MC phono-pre. But

we need to assume that cart producers know what they are doing.

MM phono stage with fixed 47k Ohm load resistors is not the best for HOMC cart, you'd better try a proper MM stage with an option to change load resistors, you will find which loading is better for your HOMC (1k Ohm was better for mine)
47K is what Hana recommends, as the("suggested load") impedance for their HOMC(SH). The output(2mV) will work with some MM stages, depending on your SPL desires and the rest of your system’s gain.

47 K is standard for the MM phono-pres. The cart producers

should follow this standard. They can't expect their customers

to mess with resistors. The most have no idea what resistors

are (grin).

According to Jolida, the JD9 II phono stage provides 60 db of gain for 5mV input via the MM section, 75 db or 85 db, respectively, via the MC low and high gain sections, for lower input voltages. (I looked but could not find any data for the model III.) If the nominal output of the Hana SL is 2mV and assuming 60 db of gain via MM for 2mV in, the output signal would be 2V. That alone is more than enough voltage to drive most amplifiers to full output, regardless of the gain afforded by any linestage inserted between the phono and the amplifier. You could even use a passive linestage. So, I would say the MM section ought to be MORE than adequate. Mark, most amplifiers are driven to full output by 1V or more of signal voltage. You need to know the output of the cartridge (typically stated for 5 cm/sec stylus velocity), the gain of the phono stage, the gain of any linestage in the pathway, the input sensitivity of the amplifier, and the efficiency of the speakers, when making these estimates of how components will match in actual practice. OR, just try it.

As to the load resistance, that is a dance that never ends, but I routinely use 47K ohms into my MC stages and 47K or 100K into my MM stages. Every time I load down even a LOMC cartridge, I find myself preferring the "unloaded" state afforded by 47K. But that’s just me and my particular (Atma-sphere MP1, fully balanced) phono stage.

Nandric, It would be impossible for cartridge makers to follow any guideline for load resistance, let alone 47K ohms. First of all, most end users are brainwashed into believing that they need to use 100 ohms or thereabouts for LOMC cartridges, and they would be put out by not having that option available. Many phono stages use a fixed 100 ohm load, because it makes the customers satisfied. As you know, many modern phono stages solve the problem by providing a choice of loads starting at 100R and going out to 47K. Most cartridge package inserts state ">100 ohms", or similar ambivalent directions. As Ralph is fond of pointing out, the load resistance is more for the phono stage than for the cartridge, at any rate.