Likely is less definite. For example, if the sky is dark and cloudy, it's likely that there will be a thunderstorm, but it might just be rainy instead of the thunder and lightning.
Certain is absolutely positive. For example, you could say,"I'm certain I'm a human" or "I'm certain I have a cerebral cortex (brain)".
"Likely" thinks it will probably happen.
"Certain" knows it will definitely happen.
Hope that helps, from PNE.
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