No, not even close.
Age of Empires is a Real Time Strategy Game. Civ IV is turn based. In AoE, you go around clicking on things and making your units move around in real time. In Civ IV, you do whatever you want to do and then end your "turn", which advances time. The AI then makes its move. It's more slow paced than AoE. It's not in real time, which means that you can take as long or as short as you want.
The objective of AoE is generally to wipe the other players off the map. In Civ, there are multiple ways to win (Conquest is one of them). Even if you're going for that, there's generally more focus on the economy and diplomacy aspect. AoE is a war game where you advance in ages, Civ is an empire building game where you can make war.
Civ IV is far more deep than age of empires when it comes to things like diplomacy and empire building, and each game of civ lasts longer generally. AoE is more deep combat-wise, and is faster paced.
Each game of Civ starts out at 4,000 BC (usually, you can set it to change) and goes up through 2050 AD (assuming no one wins before then). There are no set "ages" like in AoE. Rather, your civilization advances technologically (and you of course choose what to research).
I can't explain it very well. Your best option is to try out the Civ IV demo
here
It should give you a general idea of how the game plays out.
Enjoy!