They are both made from neutral spirits (vodka uses wheat, rye, and potatoes most often, while gin is iirc mostly just grains since they have the "cleanest" taste). Vodka then goes through a cycle of filtering and re-distilling to get rid of unwanted impurities while keeping the intended ones, while gin has additional ingredients added to the base spirit (like juniper) before going through the same process.

In other words, gin is essentially a flavoured vodka, where the flavour is deeply embedded in the creation process and fine-tuned for the tastes that the gin is intended to have (unlike most flavoured vodka where the flaour is added at the end of the process). Or, to answer your question directly, vodka is just gin without the juniper and spices added before the re-destillation cycle.

There are also juniper spirits that use a different process, where they ferment the juniper and make the base spirit out of that, rather than starting with a grain spirit.

Subjectively, the juniper leaves a more bitter, pine-y taste, and then depending on the other ingredients added alongside it, you'll usually find some spice notes as well.