It is very important to note that there are two versions of Terraria on Google Play:
"Terraria" -- This is the free TRIAL version with limited content and the option to buy the full version as an in-app purchase
"Terraria." -- This is the paid version (note the period at the end of the title)
You can purchase the full game from within the free version, but this does not unlock the storefront version (#2 above). They are two different -- but identical -- versions of the same game. The in-app purchase essentially "unlocks" the free version so that it is functionally identical to the storefront app.
If you have previously purchased the full version of Terraria from within the free app, it will appear as "Terraria Full Version (Terraria)" in your Google Play Order History, but it will not appear in your device's app list. Don't worry, though! All you have to do is download and install the free version (#1 above) and your license will unlock Terraria's full content!
Your screen should look similar to this:
If the only buttons you see are "Play", "Tutorial", "Options", and "Game Service", you're good to go!
Please visit the link below for step-by-step instructions on how to reinstall previously purchased and downloaded apps to new or factory reset devices. If you can't find an app you previously purchased, or you're being asked to purchase an app that you already bought, make sure that you're signed in with the same account that was used to make the original purchase.
For more information, please visit Google Play Help's "Reinstall apps & games" page, but please be aware that you will lose your data if you are only using Local saves with Terraria before you decide to delete and reinstall your game.