A live USB version is a bootable USB and runs Kali from a USB drive.
An installer USB version is for installing Kali to an internal Hard drive, did you download the 'bare metal' ISO?
https://www.kali.org/get-kali/#kali-bare-metal
You need to let it install all 'non free' drivers and firmware when you do the install, some of your laptops chipsets may well not work without it.
Most problems installing Linux, not just Kali are usually driver and firmware related.
