For me, they are closely synonymous. I use "concentrate" more when there is something I am doing and I need to avoid distractions. e.g. "I need to concentrate on teaching the student now" It has the extra sense of deliberately putting your mental energies into a task you are already committed to. If you are talking about a range of subjects and you think that one needs special attention now, you "focus on" it. You bring it into your "sight". So perhaps you could say that you "focus on" something first and then "concentrate on" it. "I need to remain focused on this issue" is a good expression. "Focused" here sounds much better than "concentrated".

Even when they are used in similar context, there must be some differences between them...

I use them interchangeably. To me, there is very little difference.