Is Tokyo a City in the Sense of How a New Yorker Views of a City?

I've never been there, so I'm having trouble imagining it. From what I can google, while Tokyo has a few million more souls than New York, it also seems to have four times the area. I couldn't imagine what New York would be like if there were four of each borough. So, what exactly are Tokyo and it's wards? Are the wards comparable to New York's boroughs? Please share your thoughts on how it's different from a typical city, or any other thoughts you have.