The difference lies in having the mere ability to do something and choosing to do something that you are able to do.
If he had a heart, he would be able to love.
If he had a voice, he would choose to sing.
If I had the money, I could buy it. ability
If I had the money, I would buy it. intention
Having the ability to do something does not necessarily mean that you would actually do it.
If I had the money, I could buy it. I wish I had the money to buy it! I want it!
If I had the money, I could buy it. But it is a foolish extravagance and I would never buy something like that!