Each of those terms refers to a few things, so they depend on the context.
Some examples:
Getting CPDLC-DCL (departure clearance) in USA?
That's FANS over ACARS
Automatically reporting position over the Atlantic?
ADS-C using FANS over ACARS
Requesting climb over the Pacific?
CPDLC using FANS over ACARS
Receiving reroute over Europe?
PM-CPDLC over ATN B1
Receiving load sheet?
AOC over ACARS
Depending on the plane and region, not all systems and functions may be available. I think it helps to know them top-down: what each data link system offers.
Aircraft data link systems
1. ACARS ATS
Application |
Description |
Network |
DCL |
departure clearance not used in USA (see CPDLC-DCL under FANS) |
ACARS |
OCL |
oceanic clearance |
ACARS |
D-ATIS |
data link ATIS |
ACARS |
PDC |
pre-departure clearance in use since 1991; primarily in USA; not a direct link to ATC not under 'ACARS ATS' the system but is worth mentioning here |
AOC over ACARS |
Further reading: honeywell.com and code7700.com
Pilot about to select the OCL page aboard a 747-400 (YouTube)
Application |
Description |
Network |
AFN |
ATS facilities notification the application used to log on the ATC network |
ACARS mainly oceanic |
CPDLC |
the application used for communicating with ATC |
ACARS mainly oceanic |
ADS-C |
automatic contract position reporting uses set intervals and events |
ACARS mainly oceanic |
AOC |
airline operational control the airlines' own applications (e.g. uplinking load sheets) predates and prerequisite to FANS |
ACARS |
CPDLC-DCL |
departure clearance used in USA; utilizes the FANS system and requires logging on the flight plan can indicate whether this DCL or PDC is preferred or second best |
ACARS terrestrial only |
Further reading: boeing.com
Successful logon using AFN aboard a 747-400 (YouTube)
3. FANS 1/A ADS-C
The same as the above minus the CPDLC capability.
4. ATN B1
Application |
Description |
Network |
CM |
context management: data link initiation capability (DLIC) FANS' AFN equivalent |
ATN B1 Continental Europe |
CPDLC |
the application used for communicating with ATC AKA PM-CPDLC (protected mode) |
ATN B1 Continental Europe |
Accepting a frequency change using ATN B1 aboard an A320 (YouTube)
5. FANS 1/A - ATN B1
AKA FAN 2/B, and A+B (in Airbus lingo); combines FANS 1/A and ATN B1, and is found on newer aircraft (e.g. 787 and A350), and can be retrofitted to some older aircraft (e.g. A380).
Related: What are the differences between FANS A, B, and C? Is FANS C commissioned?
The subnetworks
ATN B1 uses VDL M2: very high frequency data link - mode 2 (project's name: LINK2000+).
FANS 1/A uses VDL M0/A (AKA Plain Old ACARS – POA), VDL M2 (AOA), HFDL (high frequency data link), and SATCOM (Inmarsat and Iridium).
Main reference used: ICAO's Global Operational Data Link (GOLD) Manual (PDF)