V score: Imagine four copies of a small square layout all next to each other - created on a solid piece of FR4 material. The mfg will cut a small trench inbetween each (square) design - on the top side and the back side. You get the boards four at a time. You stencil all four at the same time, populate them, and cook them together. Once they're done cooking, you bend them at the v-score, at they'll break apart pretty easily. It's a quick and cheap way of batch building a design. This works well for boards under 4x4". The larger the board, the more likely you are to get skew problems with the PCBs, large paste stencils, pick and place errors, etc. You can either have the mfg panelize the design for you or you can layout the panel yourself. Obviously, if you need to have a stencil made, you'll want to create everything yourself so that the paste stencil lines up exactly with the panel. You can create any type panel array : 1x4, 2x23, whatever. But we've found that anything over 4x6" will irritate human assemblers cause their hand will have to hover over the PCB will placing. Not a problem if you go with an automated p&p.
Jump score : I dunno. Never heard of it before. Google would probably cover it.
Tab Routing : So if you've got a oval or funky shaped PCB, vscore cannot be done, but it's the same idea. Your funky shaped design is panelized - let's say there is an array 3 x 2 for a total of 6 of your boards fabricated onto a single piece of FR4. You stencil, populate, and cook just like before. But how do you get them apart? Before the mfg sends you the PCBs, they will route the board 95% (or so) around the border leaving two or three spots where the oval shaped PCB is left connected to the main panel. After cooking, the boards can be removed from the panel by cutting or breaking these 'tabs'. The border is smooth except for these few tab spots.
Mouse Bites : You didn't ask but you may come across it. This is just another routing technique close to tab routing. Instead of tabs, the entire border is hit with a series of medium size drill bit holes so the board is just a long line of closely spaced holes. The PCB can then be depanelized after cooking by breaking the design from the larger panel. The board has a funny border of half-holes that looks like a mouse chewed on the edge - mouse bites. This was considered a cheaper, faster option because it only used a drill bit - where the tab routing requires a mill (tool change = more time, more $). PCB routing with mill is so common now, few designs save money using this technique. Drives mfgs crazy because it wears out drill bits really fast.
Eek that was long.