I understand what is the premium on an option.
In case I acquire an option, the premium is considered as the price I pay to have the "right" to exercise the option.
In case I sell an option, the premium is the money I get from the other counterparty and he or she will have the right to exercise the option.
For these two cases, If I sell / buy the option I get, is this money considered as a premium too.
Let's say I acquire an option, paying the premium. 1 week later I sell this option to another person. Is the money received from this last person also considered as a premium?