A Kirtan and Bhajan are closely related. Both are sung, with musical instruments, use Divine Names or Scriptures, and are oriented towards creating connection with the Divine. 

I like to think of Kirtan as a short phrase (like a short sentence), sung in call and response fashion.

In contrast, a Bhajan is a longer phrase (like a paragraph), and may be more free form. 

Kirtan may be more structured than a Bhajani to maximize accessibility and audience participation. 

That's about all you need to know.