Press And Printer ,how cmm works

Hi could someone explain the correct procedure in profiling a press, printer and icc profile

my understanding of making icc cmyk press and printer icc profile
print eci target and read with spectro
wavelengths are measured and multiplied by illuminant multiplied by xyz
convert to lab for icc profile of press

linearize Printer, print eci target chat and do the same to produce icc
when you have you icc press , icc printer what is cmm that measures the two so the output is the same, printer profile will have a much more wider gamut then the press how does cmm achieve this

could some please explain in more detail or better a web page the Cmm and how it process the 2 icc profiles or the whole process