I am just giving a basic summary of these two types of players. But I understand not everyone uses just one. I think most people probably gravitate towards one of these more than the other. That doesn't mean you will never use both.
Tone Reading:
This is what I think of the more emotional side of mafia. This is analyzing someones words and seeing if they match both the context of the situation and if it matches what they are overall saying. When a person is tone reading they are looking for things that don't match in terms of what a person is feeling and saying. For instance when someone is AtE because they are being pushed. Is the AtE anger over ridiculous accusations or is it more anxiety of the whole situation and not knowing how to act? Is someone being sincere when they claim to have a scum read on another player? Are their words showing they aren't being completely truthful or trying to avoid certain subjects?
If you are a tone reader, you are trying to understand what a player is feeling and seeing if it makes sense from someone of your alignment. If I was in their shoes, would I feel and act similarly as the same alignment?
Motive Reading:
This is what I think of the more Logical side of mafia. This is analyzing someones words to what exactly are they doing. If you are motive reading, you are trying to see each step. What is it are they doing and why? You might see someone pushing someone for a lynch and think, well why does this person want to lynch this person. Do they really think they are scum or is it just something there to distract. If someone claimed something, why did they claim this? Are they in danger of being lynched? Did they make it just because it was easy information to give out and didn't hurt them either way?
If you are a motive reader, you are trying to see if what they are doing is something that makes sense as someone of your alignment. Are they doing something that will logically help your win condition?