Notwithstanding the variation in terminology evident on Wikipedia, the general convention is that "Breadboard" refers to the plastic socket board, and "Protoboard" refers to a PCB whose tracks are laid out to emulate those on a breadboard, including the common "bus" strips on each side.
So both of what you illustrate, are breadboards, one without and one with the "bus" strips, while this is protoboard:
(With a mini-breadboard on the right for comparison. :grinning: )
Oh! Which one should you buy? Both, of course! The big one with bus strips, and a couple of the tiny ones. You can't have just one Arduino either! Silly question! :grinning:
The Nano is the better Arduino for use on a breadboard.
Note also something funny about those large "MB-102" boards - some have the bus lines connected all the way along, some have all four bus lines interrupted in the middle - it is indicated by the continuity of the red and blue lines. It is probably rather unusual that you would not want them running all the way along.