The Raspberry Pi is a tiny computer, and you can add a screen, keyboard, mouse etc
Once set up as a little computer it can be run and used on its own.
But it first needs to be set up with an operating system, and unless pre-set you would need a seperate computer to download the operating system etc
The Pico is a mini Pi, with less capabilities and is a micro processor with connection pins intended to be the core to build projects. (The Pi can also be used as the core to projects)
The Pico needs to be used alongside a computer to enable you to configure and programme the Pico.
A similar thing is the Arduino, this is a microprocessor with various models and sizes for project needs.
I’m no longer familiar with the Raspberry Pi, having only the original model. This needed an SD card to run - all software is loaded from the card as it starts up (so you can use one Pi with different cards booting up for different purposes). Newer Pi models have internal memory
I spent quite a bit of lockdown experimenting with Arduinos.
I have the standard Arduino Uno which is similar to a Raspberry Pi, plus a large Arduino Mega which has more memory space and more connections plus Nanos which are small with less memory and less connections - the Nano is like a Pico
With the Arduino you programme on a computer then download into the Arduinos internal memory
Your existing ‘old and slow’ laptop can probably be used to programme Pis / Arduinos. But with the Pi he could ‘build’ a new computer - it still wouldn’t have the range of capabilties of a laptop / computer but they are capable of many things
https://www.makeuseof.com/tag/arduino-vs-raspberry-pi-which-is-the-mini-computer-for-you/
It will be worth checking in with the school on what he uses and will use at school, and then getting set that guides through a series of projects.
There are various sets that contain the Pi/Arduino plus components to build a range of projects to learn to use them.