Single plate black means the shade of black is made from ONLY the black printing plate. Being K from the traditional CMYK.
Rich black means the shade of the black is made from a composite of CMY and K plates. The exact combination varies, but a fairly common one is photoshop black 75, 68, 67 and 90. Using more cyan though would result in a cooler black whereas more magenta would mean a warmer black.
Misalignment that can occur from mixing multiple colours together in print will 100% not happen from a single plate black.
Plate black will not be as full as a rich black.
To see rich colour on indesign you click on Indesign CC in the top left hand corner → appearance of black → change both to display all blacks accurately/output all blacks accurately → OK.