1. His hand is sticky.

2. His hand is slimy.
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Are both the same in meaning? Which one is commonly used, 'sticky' or 'slimy'?

They do not mean the same thing.

https://www.dictionary.com/browse/sticky

https://www.dictionary.com/browse/slimy?s=t
and
https://www.dictionary.com/browse/slime?s=t