Why are sticks called sticks if they're not sticky and other things that are sticky aren't called sticks?

In every language, there are pairs of words called homophones.  These are words that have the same sound but which have different meanings.  Languages are very likely to have such words because there are not all that many possible sound combinations and there are huge numbers of words in most languages.  Therefore, it is not at all uncommon to have words like this that do not have the same meaning even though they sound the same.  As you can see in the link below, by one count there are 441 pairs of homophones in the English language.

Other languages have homophones as well.  For example, in Japanese, “hashi” can mean “chopsticks,” but it can also mean “bridge.”  As another example, in Spanish, “llama” can mean “call,” but it can also mean “flame” and “llama,” the Andean animal.

In other words, it is not at all unusual for there to be words that sound alike but which mean very different things.  Therefore, we should not be surprised that sticks are not sticky.