Do not buy anything if you're unsure how it works or whether it's compatible.
Just taking a quick look at the MS20 (mini) recreation that Korg is selling I'm not sure whether the Keyboard transmits MIDI. The unit receives MIDI but the keyboard may not transmit it. For that amount of money you could purchase a keyboard that did a lot more. The MS20 may be cool but it's extremely limited. (Extremely!)
First educate yourself on what MIDI is and how it works.
The first sentence in the paragraph below is a key concept. MIDI IS NOT sound, it's a very small set of instructions that describe a performance. (what note you played, how long you held the note, how hard/fast you played the note...etc..etc.
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MIDI, which stands for Musical Instrument Digital Interface, is a computer language that conveys musical instructions. For example, when a MIDI keyboard is played, messages are sent which describe what notes are played, how long each note is played, and much more. This information is sent to other MIDI instruments or devices where it's reconverted into music. All kinds of electronic instruments, and even acoustic instruments such as pianos, guitars and windblown instruments, can be equipped with MIDI capabilities. MIDI sound modules, keyboards and sequencers are all considered musical instruments since they all contribute to the creation of music.
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This performance can then be played back any type of MIDI instrument that can receive MIDI and produce sound. The sounds in the MS20 are not magically transmitted "into" Logic, the synth produces the sound out of it's audio outputs. The sound can be recorded in Logic just like you would record an acoustic guitar or voice.
Like I said, the MS20 is very limited and the keyboard doesn't transmit MIDI so you couldn't even use it to play Logic's instruments. It not what I would buy.