To do with reactivity, I think

[Kyoma]

1) If you connect zinc and copper with a wire and submerge them into aqueous sodium chloride, a reaction will occur, such that there is a potential difference between the metals. Why? Aqueous sodium chloride is not an acid nor is sodium less reactive than zinc/copper such that zinc/copper would displace sodium from its solution.

2) If you add zinc oxide (solid) into sulfuric acid in excess, the final pH of the solution would be slightly higher than 7. Why? Zinc oxide reacts in the acid to form zinc hydroxide and water, which are of pH 7 and that zinc oxide in its solid form is also pH 7.

 

[Nemus]

You always need to consider all species in the mixture in cases like these.
1. The metals in contact with a liquid will be in equilibrium with the free ions. Zn will give off some more than copper. If the electrodes are not connected to anything the build up of electrons stops the reactions at a very early stage. If you connect them electrons will flow from the more electron rich side (Zn) to the less electron rich. You can probably work out the details or keep asking and I'll expand on hydroxide formation etc.
Zn <-> Zn2+ + 2e-
Cu <->Cu2+ + 2e-