As you gain more experience with your medium format equipment, you may also find that your prefences are different in respect of development times.
Your 35mm camera may have lenses that are more (or less) contrasty, the multicoating may be more (or less) effective on the medium format lenses, the meters you use may difffer between the formats, the shutters may be either faster or slower in one camera vs. the other - in short you may eventually find yourself fine tuning the development for medium format film in different ways than for 35mm film.
The film itself is usually on a somewhat different base - for that reason it feels a little bit different to work with when you are loading it onto reels. It is not that you need substatntially different equipment, it is that you need to adjust to the way the film reacts when handled.
I note that you made reference to 220 film in your original post. As 220 is twice as long as 120, you need to make sure that the reel you use is suitable - some 120 reels are not.
There is one thing that is different - you need 120 negative sleeves - the 35mm won't work
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Have fun!
Matt