Based on #12237 I made similar changes to descriptions of value_template and payload_xxx.
Changed/added some comments as terms like 'availability state' are really confused, maybe it's better not to use them?
Not sure term "payload" is used correctly as it's difficult to find difference between message and payload so I went ahead and used "message" and "string" appropriately.
Also fixed some On/on/Off/off descrepancies.
It's all based on my personal experience/posts on the forum/source code.