When you create and edit a Metarig, you are creating a simple placeholder that will mark some locations in space, the Generate rig function will then create the actual rig, which is quite complex because it has a lot of useful functions.
Basically different kinds of bones are created: counting bones layers from 00 to 31, in the 31st layer you will find a copy of the metarig bones (ORG suffix), in the 30th some machinary bones that are supposed not to be touched by the user (MCH), and in the 29th layer all and only bones that actually deform the character (DEF).
All others layers contain nothing but control bones, which do not show as classic octahedral shape: they use all widget meshes (WGTS) to better suit the needs of animators to watch their model while animating. So in the WGTS collection there are meshes, not bones, as you can tell by their orange triangle icon in the outliner (bones have green bones instead).
The correct way to export a rigify animation is to perform the actions into Blender, when finished create an animated copy of the rig, go to 29th bone layer, select all DEForming bones, go to pose mode > pose menu > animation > bake action (Clear constraints, visual keying, overwrite current, clean curves).
In this way you can delete all bones that are not in the 29th layer and export a simple deforming rig that doesn't refer to any special Blender function (like constraints or drivers) and can be easily used in game engines or others animation softwares.
FK stands for Forward kinematics, and it's the process in which you move and rotate a chain of bones one by one until you reach the desired pose.
IK is Inverse Kinematics, in which you move an end of a bone chain (i.e. a foot) and all the chain follows that movement (i.e. all the leg). Both are useful, so Rigify lets you switch from one set to the other.
