Using an original iPhone charger (typically 5W or 12W USB power adapter with a USB-A to Lightning cable) should not harm your iPhone 14 or 13 Pro’s battery. iPhones are designed to be compatible with a range of chargers and have built-in protections to prevent overcharging.
The main difference between the original charger and a Lightning fast charger (usually a higher-wattage USB-C power adapter with a USB-C to Lightning cable) is the speed at which they can charge your device. The fast charger, as the name suggests, can charge your iPhone more quickly.
However, do keep in mind that while fast charging can be more convenient, repeatedly fast charging your iPhone may cause the battery to degrade slightly faster over time compared to regular charging, due to increased heat produced during fast charging. This is a normal behavior for lithium-ion batteries.
That being said, it’s important to use only Apple-certified chargers for your device. Non-certified or counterfeit chargers could potentially damage your device or its battery.