So can anyone differentiate Latin and Modern Dance of Tango?
Well, yes. Assuming that by "modern" you mean "Standard," Tango is one of the five dances in the syllabus. Because Tango music - and dance - have Latin origins, it's easy to see how someone could think that it's a Latin dance.
There are also Smooth (American) Tango and Argentine Tango.
You can find videos on this site for Modern and Smooth Tango (and posibly Argentine - I haven't looked). These will give you the appearance of the dance and introduce you to the basic steps.
If you need to learn some Tango then you need to find a professional immediately and start taking some instruction. You aren't going to learn how to Tango on this board or using a video.
If you can't afford a pro then try to find a sympathetic friend who has some exposure to the Tango. As the old saying goes, you're going to need a partner anyway.
Dancing is not a skill that one picks up overnight. Whatever it is that you need will require some work on your part.
jj