Is the root file different if a custom rom is installed?

basically root method is pretty generic. the leading tools are

• Magisk


• SuperSU


• phh's SuperUser


• AddonSU

in that the order, where former one is recommended for all devices and ROMs while the last is ROM specific

However, while the rooting process is nearly the same, every device is different and there is no generic root method. First you need to unlock bootloader. Some vendors (like Huawei) decided to lock devices completely, others (like Samsung, Xiaomi, Lenovo) have there own special protections

Second, you need custom recovery (or at least, modified boot.img) which is definitely device specific and not interchangeable with other device models

Usually every device has it's own section in famous xda forum where developers share custom recovery or custom rom

Always search for root method specific for your device model

(Note: i am aware of exploit based temp root methods but decided that is out of scope and not worth a timeless answer, because development is ongoing and that exploits become outdated)