One is the temporary hack and other is the permanent one.
In temporary hack, PSP runs the custom firmware as long as its switched on/standby but after restarting it, things go back to default.
In this page I’m describing the easiest possible way for you to install the most reliable Custom Firmware on your PSP: Pro CFW.
It does not require any advanced hack technique or hardware modification.
If you are interested in the “advanced” Pandora Battery method, please go check that guide, or the “Power users” section below.
If, on the other hand, you want to follow the easy method (which for now I recommend), please keep reading.
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The Play Station Portable system software is the official firmware for the Play Station Portable.