Handycam or Photo Camera?

I am looking into buying a camera that can be used for both photo shooting and video shooting. I was going to consider a photo camera, but then a thought crossed my mind why not handycam?

Would you explain to me (as a layman) what are differences between a still photo shoot camera and a handycam?

I will use it for personal purposes; family photos, my drawings and paintings, and shooting some videos. I like HD better.

Here are two of Sony’s handycams (one and two) that look attractive to me considering the price range. My budget is around 20k to 30k Indian Rupees.