The physics
Resistors in a line carry one current. Their resistances add.
R = R₁ + R₂ + …
Resistors side by side share both their ends. The same voltage sits across each one. Their reciprocals add.
1/R = 1/R₁ + 1/R₂ + …
A bare wire joins two points into one. You can merge points at one potential. A wire between two such points carries no current, so you can remove it.
An ohmmeter pushes a test current in at A and out at B. It reads the voltage per ampere between them.