The time setting of verse 1 is Christ's ascension to heaven after His resurrection. This is when the Father said, "Sit at My right hand, till I make Your enemies Your footstool." That is when Jesus rose and ascended to heaven and sat down at the Father's right hand. In the second verse the time setting moves forward to Jesus Christ's second coming. It is very quick. You go from AD 31 to whatever the time will be 2,000 years later roughly. And at that point the Son—the Word, Jesus Christ—is King of kings and He rules on the earth amidst the nations that tried to fight Him. And it says here that He will rule out of Zion, out of Jerusalem, and from there His sovereign might goes out. "The Lord shall send the rod of Your strength out of Zion. Rule in the midst of Your enemies!" And we know that He will come down on the Mount of Olives, and He will fight against His enemies that come against Him.
So these two scriptures, two passages, say essentially the same thing, just the one in Psalm 110:2 is a little bit more concise, but they are talking about the same time, the same activities, when the Son is on His throne and He begins to fight against His enemies.