You can get IO devices that have both HDMI and SDI - it will be dependent on what the camera itself has a connection for output. And unlike some dedicated external recorders, MC does not support any embedded file naming or camera START/STOP commands. It will all be manual. And if capturing directly, original camera filename may not be needed, but you sure do need a quick backup solution when doing so.
HDMI allows for bandwidth than SDI depending on the version of HDMI being used. HDMI 2.0, for example, has 3x the bandwidth of SDI. Depending on the format, SDI will eventually need dual or quad connections.