Are laptops like mobile smartphones, can charged via USB-C chargers even from other brands chargers

Dell Vostro 5370

https://dl.dell.com/content/manual33154277-dell-vostro-5370-owners-s-manual.pdf?language=en-us

I have ordered this from www.eBay.com used good condition... however the charger is USB-C but says hp brand 45W... I have tested and charging ok...
Seems the Dell laptop 💻 has charger dedicated slot rounded and also can be charged via USB-C... however since was in used contition, the only charger is USB-C and the charger brand hp not Dell... how I know this USB-C charger is OK for this laptop 💻 longevity of battery and laptop? 

Are laptops like mobile smartphones, can charged via USB-C chargers even from other brands chargers?

DELL VOSTRO 5370 13.3" FHD INTEL i5 8150U 8GB 128GB SSD WIN11 HDMI Notebook
on eBay!