Perlite & Vermiculite are both volcanic in origin and both are put into potting mixes to provide additional air space and to lighten things up so the soil is not too dense and heavy for the plants roots.
Perlite does not provide any nutritional benefit and can collect fluoride if the water contains it. That means that flouride will increase in concentration after a while and can burn the leaf tips of some houseplants. It is rarely a problem with any outdoor flowering plants, so don’t worry if it is in your potting soil unless you are growing indoor plants.
Vermiculite is a bit different in that it holds a lot of moisture and can also hold onto fertilizer for a period of time. This helps to keep the nutrients around the roots of your plants instead of washing them out the bottom of the pot when you water or when it rains. Vermiculite would be good to use in outdoor pots that tend to dry out quicker in the heat as it retains moisture and nutrients the plants need.
Perlite and vermiculite are both good at retaining water, but vermiculite acts more like a sponge, holding much more water than perlite and offering less aeration for the plant roots. Perlite retains water because of its large surface area with nooks and crannies available for water storage. Because it is porous it allows excess water to drain more readily than vermiculite and improves soil aeration.
What you use as an additive in your soil will depend on what kind of plant you are planting. Water loving plants would do well with vermiculite, and those plants that prefer drier roots, would be better with perlite as it drains the water away better.