'Thought' can be a noun or past tense of 'to think':
- She thought about her dog.
- He has a lot of thoughts in his head - 'thoughts' in this case can mean 'ideas'
Thinking is the *act* of thinking. Can be used like this:
- She is thinking about her dog.
- I don't know what he was thinking.
You can sometimes hear people say things like 'My thinking on this isn't complete." - meaning they should think about something more.