Yes, the setup of the buttons and functions is subtly different.
The 320 has VNAV-DES and VNAV-APCH as two standalone features. The VNAV-APCH (+LNAV) is armed with the APP push-button from the MCP.
If the selected approach in FMGS is ILS, however, that APP button will arm LOC and GS instead of LNAV+VNAV-APCH.
We do have a separate LOC button, but not a GS one.
I have no knowledge or experience with the more recent 'FLS' mode for APVs.