to solace and to console are pretty much synonymous: trösten
to comfort can mean different things, from being synonymous to "console" to "giving strength and hope" (to ceer).

Is there really no difference between to solace and to console??? When would you use which one?

It may be that "solace" is a bit outdated; I don't ever see it in writing. "console" is usually used, so you can't go wrong with that.

Agree, I do think "solace" is quite old-fashioned, or at least religious. I think of it as having a spiritual connotation. And I think it's more common as a noun:

After the devastating floods, parishioners flocked to the church in hopes of solace.
He consoled the child after her dog died.
The baby was fussing, but I comforted her with a blanket.

"Comfort" can be about anything from physical to emotional circumstances. "Console" is emotional, used for grief, bereavement, pain, or trouble.

'Solace' is very uncommon or oldfashioned as a verb. I think you can safely forget it and just use the noun.

'Console' is usually for a loss, such as a death or a large financial setback. It's more analytical and general, trying to make the loss seem less negative, looking at the bigger picture or seeing the positive side. When a child's pet dies, his parents try to console him by saying that the pet lived a good life and didn't suffer at the end, that pets just don't live as long as people, and that he can have another pet someday.

'Comfort' can be for other kinds of pain or fear. It's more personal and emotional, just trying to make the person feel better right away. When a child is hurt or has a nightmare, her parents try to comfort her by holding her tight and telling her everything will be okay.