Let's see if we can get this straight. I'll draw you a little diagram:
|###| ______________
____ |###| | __________ |
|////| |###| | | __ | |
|////| |###| /| | \\ | |
|////| |###| / | | \|| |
|////| ___ |###| / | | | |
|[u]DELL[/u]|__/ \_|###|_/ | | | |
|###| | |__________| |
This is |###| | |
your server. |###| |[u] COMMODORE 64 [/u]|
|###|
|###| This is your computer.
PHP runs on your server. In this diagram, it's the little box that says "DELL."
The client is the shiny box that says "COMMODORE 64." Top of the line equipment. This is where popups and javascript exist. They have nothing to do with the server.
There is a big wall between them. It can range from several inches to several thousand miles (for ye non-Americans: several centimeters to several thousand kilometers).
Hope you enjoy the diagram.