Yes .. and no. While the salt itself can be considered the same, it's the impurities contained in the crystals which add color and flavor, and the rarity of some salt, that drives the price of the specialized or "boutique" salts. By rarity I mean that some salt is found only in limited or specific locations, quick off-the-top-of-my-head examples would be Himalayan pink salt, French Grey Sea Salt (Sel Gris de Guérande), or Hawaiin salt which has lower levels of sodium chloride and up to about 15% of other minerals.
While the salt in some ancient mines is the same, or very similar to, sea salt, that is not the case with all ancient mines. The Khewra mine in Pakistan produces a decidedly different salt, the renowned pink Khewra salt. There are quite a few ancient mines around the world and they don't all produce a clone of Atlantic Ocean sea salt.