The tiers of ores in Terraria are Powder, Copper, Tin, Silver, Gold, Platinum.
The higher tier a select ore is to collect and smelt for use in equipment building the more valuable it is.*Working Hard Mode refines the tier of some items by changing all tiers within that material’s chart (Tin up to Platinum).*Powder never changes anything and can be used freely without restriction therefor as long as you have Ores.
*For example using a Standard hammer on any Iron Ore will give you 3 Iron Bars per refining but using a Mythril Hammer wont yield any upgrades or add benefits to your hammers or work while wasting time crafting an expensive hammer.*This is just one example such as refining Tin Ore with a Mythril Hammer will upgrade it to Copper giving you 3 more bars.
Mythril is the strongest material that can be mined below Adamantite Ore being able to produce 5 Bars per ore that it receives as Powder.
Finally, yes there are alternate sources of obtaining ores rather than mining them but their availability varies.