Is the 737's autopilot part of the FMS or is it a separate entity?
In Boeing terminology, the FMS, Flight Management System, is comprised of:


Flight Management Computer System (FMCS, which is essentially two FMC's, at least on the 737... other jets may have one FMC, or three)
Autopilot
AFDS (Autopilot/Flight Director System - includes the Mode Control Panel used to select autopilot modes, heading, speed, altitude, etc)
Autothrottle
GPS(s)
Inertial Reference Systems (IRS)
Two (in the 737, three in some other jets) CDU's, which are the "Control and Display Units" with a small screen display and alphanumeric keyboards, used by pilots to view, enter, and edit things such as flight routes &amp; performance data. Many such units are now "Multifunction CDU's", or MCDU's, adding ACARS and/or CPDLC capability.


So in their terminology, the FMS is very broad and includes plenty of things, including the autopilot. The FMC, on the other hand, is the computer that stores your route, calculates the aircraft's position (based on inputs from the GPS receiver(s) + the IRS + possibly other sensors), and does all the navigation tasks. One can couple the autopilot to the FMC guidance - select LNAV and/or VNAV - or not.

It's not uncommon to hear or read "FMC" and "FMS" used interchangably, but they are in fact two separate things. The FMS (the system) includes the FMC (the computer) and the autopilot; the autopilot can be coupled to the FMC, but it is always a component of the FMS.

Sometimes you'll see a CDU referred to as "the FMC (or FMS)" since the CDU is the pilot's main interface with the FMC. But they are separate things; you can have a CDU failure with all FMC's still working, and vice versa.

Clear as mud?