What is the difference between "FS Device", "FS Device/Host/OTG", and "HS Device/Host/OTG"?
Any USB cable can be plugged in or out at any time.  Part of the design.  Has nothing to do with OTG (see below).

FS stands for "full-speed", 12 Mb/s (USB 1.0/1.1).

HS stands for "high-speed", 480 Mb/s (USB 2.0).

There is another higher speed in use, "Super-speed", which is 5 Gb/s (USB 3.0).  Higher speeds still (e.g. 10 Gb/s) have been announced, but I'm not sure there are any products using them.

The Host is the electronics that is controlling the conversation between it and the slave device. A typical Host is a PC or laptop.

A Device is the electronics that is being controlled by the host.  A typical Device would be a PC keyboard or mouse, USB flash drive, disk drive, smartphone, or a DVD player.

OTG as you guessed is "on-the-go".  But it means the electronics can act as either a host or a device.  An example is a smartphone, which can act as a Device when connected to a laptop, but a Host to other devices.