Does pinching (using fingernails) or pruning (using a scissors or shear) affect an indoor houseplant differently ? And which method should I use with herb plants like mint and basil ?
Herbs are very resilient plants and grow in many conditions, I usually pinch my mint and basil out of convenience (Can´t bother getting the scissors)
For more delicate plants people prefer the scissors to minimize the wound area to prevent issues.
So, I believe the differences between pinching and scissors are, cleanliness, usually scissors are easier to keep sterile and they produce a smaller wound area on the plant so its less likely to introduce some kind of infection.
It depends on the plant type. For example with bonsai it is recommended to pinch conifers (pines) instead of cutting them with scissors. The reason is that you can cut needles in half and they will die off (turn brown), so this is for esthetic reasons. Deciduous trees are usually trimmed with scissors.
For herbs like Basil, I find it easier to use my fingers instead of scissors, pulling off a few leaves is easier than using scissors (is my opinion).