Is taking a video technically also taking pictures?

Technically yes because a video is nothing more than a bunch of photos being shown in repaid succession usually around 24 frames per second.

Photography is the art and science of reproducing images of objects on surfaces sensitized so they react to light or other radiant energies. Photography encompasses exhibiting images. Photography is a vast field ranging from a snapshot in the backyard to movies and TV and the surveying of astronomical entities. Photography envelops medical imaging (X-ray) and the making of computer chips as well as fabricating minuscule machine parts. Buckle your seatbelt, you ain’t seen nothing yet!       

Currently all moving image recording systems do it in frames, a series of still pictures.

Yes, that's why the police say they've arrested someone with 10,000 illegal images, they mean a video.

For most legal definitions 'photography' covers any film or digital capture including video. Rather depends on the particular jurisdiction, but most would regard single frames as photographs.

old movies that used film had pictures.  "Filmed on tape"  Or some sort of hard drive or solid state memory has no actural pics.