Why is "Fearing the Lord" equated to loving Him?

This question is probably more directed an Old Testament pattern of a description of our attitude towards the Lord. I equate "fear" more closely with "hate". For example today there was local news that a mountain lion "may have attacked a pet dog". That fear factor would lead to efforts to have the mountain lion _killed_. That's pretty far from love. Let's go an assumption (that I made up) that "fear" were intended more closely to "respect". That may be the case but one can just as easily respect someone you love as someone you fear. Are there multiple words/nuances of _fear_ in the Biblical languages (Hebrew? Greek? Aramaic) ? Similarly are there some aspects of the Biblical Hebrew culture - or even more generally Semitic/Middle Eastern culture - that explains why "fear" is chosen as the way to instruct/describe the attitude/disposition to the Lord?