Could you explain difference between them such as usage? In my dictionary, both have almost the same meaning. I cannot understand exactly.
Approbate means "to officially authorize" while approve means "agree or accept". Approbate is very formal and rather uncommon, and is usually used in official contexts such as political proceedings. Additionally, approbate refers more to the action of approving whereas approve connotes an attitude or sentiment, especially a moral judgment. Approve can also be used in context to mean "officially approve".
"I don't approve of such revealing clothing."
"The chairman approbated our request."
"This order needs to be approved by a judge before it can be carried out."
I'm not very familiar with the word "approbate" so I might be missing some of the nuances. As far as I can tell, they mean the same thing, but approbate is far more formal.
For example, I might approve of a new law, but that doesn't mean it is any more or less likely to become a law. But if the government "approbates" a new law, this new law is now legally and formally approved and is the law.
As for usage, I would recommend almost always using approve. You can use "approve" anywhere you could use "approbate" but definitely not the other way around. For example:
I'm DJMcMayhem, and I approbate this message.
Sounds very strange. I would also recommend "approve" since it's a much more common word.
As you say, they both have pretty much the same meaning. They have come, via different routes, from the latin word probere, meaning to test. Approbate is slightly more official in meaning, and many english speakers would have to look it up in the dictionary to be sure of the meaning. Firefox spell checker isn't to sure about it either :-). If you want to be understood, I would stick to approve.
It's worth noting that the expression "approve of" has a slightly different meaning. Here are some examples:
The government approved the new construction project. The government approbated the new visa requirements.
Governments are involved, they have made a decision: something very important is about to happen.
My boss approved my expenses
This is only a small decision, but something is still going to happen as a result of it.
He approved of her taste in music.
He has no control over her taste in music, nothing will happen as a result of his approval, but he likes the kind of music she likes.