I am trying to wrap my head around modules and partials. To me, both are same thing - you call & display in certain place content from another file.
Can you give me a clear example when one has it’s advantage over the other? What are good use cases for each?
If i understand you right you’re trying to find out what’s the difference between _modular files and twig files included into your template? If yes the big difference is, that the _modular pages aren’t static like the partials which you’re including hardcoded in your template. For example you’re able to access the _modular's content in your Admin Pugin. If you want to have changes in a partial you have to go in your templates and do them there.
@chidvanid give me some more specific example how would one benefit from having _modular files? What cool things I can do with them? 
Are there any themes/sites out there that demonstrate nicely power of _modular content?
Modular pages consist of sections with different layouts (say, three columns of text, image on the left with text on the right, image gallery, hero banner image with a heading and a button, and so on) that you can build new pages with simply by adding markdown files and folders — no need to touch the template twig files.
to give you a little example, look at this page. Every section is a _modular page. The good thing is, you’re able to rearrange delete or add _modular pages wherever you want to in a template under those the _modular pages listed (In case you’re rendering the _modulars in the parent template).
So you’re much more flexible with your templates and you doesn’t need to create many more static template files if for example the ordering of the sections should be different. The parent template from the example above uses the same template as this even if the content is such different.