This is a little like asking for the meaning of "cat", "serval" and "ocelot". Most people know that ocelots and servals are types of wild cat, but couldn't distinguish them.
Frost is a general term for the ice that forms on many things when the temperature is below zero. This is normally the word to use. It is distinguished from "snow" (which falls from the sky) and the ice that grows on puddles, ponds, and lakes.
Hoar, or hoarfrost is a type of frost. It has a "feathery" appearance. It forms when water vapour changes directly to ice.
Rime is a type of frost, it forms when water droplets in mist touch cold objects and freeze. It tends to be harder than hoar. It can also be a verb meaning "to cover with frost"
In non-technical language, there is a lot of technically inaccurate use. Most people don't inspect frost closely enough to decide if it is hoar or rime, and don't really know the technical definitions. In your examples, the window ice isn't technically hoarfrost, and it is common enough to see examples like "rimed with hoarfrost".
So for many people, these are "types of frost" but they don't know the difference between them.