What version of Minecraft am I playing?

Solution 1:

You're playing Alpha (aka Survival).

"Survival test" is here and Classic (aka Creative) is here. Neither needs a premium account.

Here's a bonus chart of what version added when in Minecraft:

   Classic    Graphics, Water, Lava, Fog, Mobs, Saving, Clouds (free)
      ↓
SurvivalTest  Health bar, Enemies, Weapons, Finite inventory, Cracking (free)
      ↓
    Indev     Crafting, Dynamic light, Night, Armor, Healing, Hell (unavail)
      ↓
   Infdev     Infinite maps, improved caves, finite water (unavail)
      ↓
    Alpha     Redstone, Boats, Carts, Biomes, Nether, Survival Multiplayer
      ↓       
    Beta      Creative mode, Weather, Structures, Hunger, Experience, Maps
      ↓
     1.x      Endgame, Hardcore, Potions, Enchantments, Repairing, Superflat

The Minepedia has more information (Classic, Survival Test, Indev, Infdev, Alpha, Beta, Minecraft 1.0, Version history).

Solution 2:

Classic:
This is the previous free version.

Alpha - Survival:
This is the one you have now, the single player is survival mode.

Check the text under the header logo here: