You could track, trace and monitor someone's movements.
You can also trace someones movement back in time. You could also trace your ancestry.
You can only monitor someones behavior and conversation.
If you are a country or big internet company, you could track, trace and monitor somebody on the internet because we are talking about their movement over the internet. Again, if you were following what the person actually did on each site, you would be monitoring them, as opposed to both tracking and tracing.