If A and B are on one street and C is around the corner on another street, then those are considered two different city blocks. The 1500 block of N. Wells St. (where all of the addresses can go from 1500 to 1599) is perpendicular to the 200 block of W. North Av. So those are considered two different city blocks.
But businesses that are across the street from each other are on the same “block.” Usually the odd numbers are on one side of the street and the even numbers are on the other side. So, for example, 1552 N Wells St might be across the street from 1549 N Wells St, but they’re on the same city block. But 219 W North Av is around the corner (and therefore on a different block) from 1552 N Wells St.
Also, the 1400 block of N. Wells St. (where all of the addresses can go from 1400 to 1499) is on the same street as the 1500s, but it is on a different block. They’re called blocks because one street runs through another street (street X runs between and perpendicular to two sections of street Y and vice versa), so the sidewalk stops where street X crosses street Y, and then the sidewalk begins again in a new block.
So when people say, “Let’s walk around the block,” (let us assume, for example, that they stepped out the front door of a building and turned left to start their walk) they’re walking up the block of one street, then left, up the block of another street, then left, down the block of another street, then left, down the block of another street, then left, back up the block of the street where they started. That’s because that entire square that they walked around is considered a block, but each side of the square is also called a block, while two parallel sides of two different squares that are across the street from each other are also considered to be on the same block. (And if you want to be technical about up and down, up the block is the direction where the address numbers go up, and down the block is the direction where the address numbers go down, but most people don’t consciously think of that when they say ‘up the block’ or ‘down the block,’ so those expressions are kind of interchangeable.)
I agree that the terminology can be a bit confusing if you think about it too hard. You would think that only the “square” would be called a “block,” but that is not the case.