Yes, it is quite different. To 'approve of', is to agree with, or in simple terms, to like. To 'approve' is to sanction, or allow. So only someone or something that has some authority can approve something. So - theoretically - someone could approve something, even though they don't approve of it! That might happen if (say) there was some political pressure to allow it, even if they don't like it.

To "approve of" means you agree with something. To simply "approve" means you give permission for something to happen. You can approve of something, but not have the authority to approve it; likewise, you may not approve of something, but be required to approve it if it's your job to do so.

When adding "of" to "approve" will indicate that it's more opinionated really. "Approve" without "of" usually indicates that you are subjecting a regulation. "The bill had been approved by congress." "The citizens did not approve OF the bill passed by congress" or "The citizens did not approve OF the bill that the congress approved." Hopefully this helps a bit.