That's a seated overhead press, I believe. Clean and jerk is an entirely different movement, and very complex movement in terms of form and technicality (ie, the type of movement you find an Olympic Weightlifting gym to teach you to do properly, or risk doing longterm damage from poor form).Military presses are usually done sitting down aren't they? Otherwise it's a clean and jerk or something. They use weight stack machines at the gym for a reason, they work. I like free weights but unless you have the room and a big selection you spend to much time swapping plates around. A weight stack machine takes a second to change.
I don't have much room, since the tool collection has grown I had to let a Bowflex go. It was that or a motorcycle!
Military press is performed standing, with the barbell in a racked position. You can either get it there by cleaning it from the floor, or taking it from the weight rack, your choice. Some people recommend to clean between each press to give your shoulders some breathing room in between presses, depends what your goals are. For straight hypertrophy you can just keep pressing and get your "pump" on.
I'm a fan of the time to take a breather and move some plates around, if I'm lifting weights they're usually as heavy as I can go on that particular day. For full body movements longer rest periods between working sets are usually recommended, give your body time to catch up with itself kinda thing. Swapping plates around gives me a chance to remind myself not to do anything stupid and hurt myself by going too hard when I'm trying to go hard.
But then again, I could just be defending myself because I have weights in the basement and don't want to spend money at the gym, or leave my house in the winter.