Did the coins at the time of Jesus have distinct images and inscriptions?

At Matthew 22:18-21(NIV) we read: "... But Jesus, knowing their evil intent, said, “You hypocrites, why are you trying to trap me? Show me the coin used for paying the tax.” They brought him a denarius, and He asked them, “Whose image is this? And whose inscription?” “Caesar’s,” they replied. Then He said to them, “So give back to Caesar what is Caesar’s, and to God what is God’s.” My question is : did the coins used by Jews at the time of Jesus bear two different types of images and inscriptions in order to indicate the usage meant of the coin ? To elaborate, were there distinct images and inscriptions on the coins meant for being offered at the Temple of God ? What were those like ?