The same 5V is paramount. But as you ask, what about the difference in the current ratings?
Charging these Li-Ion batteries requires an active circuit to monitor and regulate the charging current and voltage, else the battery may explode. It is not like the crude and cheap chargers for NiCad batteries that I have seen all the time on cordless tools.
A single Li-Ion cell has a nominal voltage of 3.6V and the charging circuit has to regulate the voltage down from the 5V. The current also has to be throttled according to the battery state. In the old days, I have often seen this regulator circuit being inside the charger. Nowadays, this regulator circuit is inside the phone itself.
Plugging a 1A adapter into a phone that uses only 0.7A wouldn't hurt. It is not likely to charge any faster either, because the regulator won't let it.
The other way of using a 0.7A adapter with a phone needing 1A most likely results in a slower charge. It shouldn't hurt the phone but may hurt the charger, depending on its design. If the designer does it right, the adapter should shut itself down for self-protection if the current demand is too high, or simply limits itself to 0.7A. After all, its cord may be shorted out accidentally by damage, or it may get plugged into a broken phone with a short. In most likelihood, it is OK (but don't sue me please).
"Old age is the most unexpected of all things that can happen to a man" -- Leo Tolstoy