Yes, there is. 'Pickle' is an general English word for any kind of sweet/sour/spicy preserved vegetable, or vegetable-based relish, usually preserved in vinegar. The word can be countable, as in 'I want a pickle' / 'I want some pickles', or uncountable 'I want pickle'. As a countable noun, it's probably a single vegetable. In US English, 'a pickle' refers to a pickled cucumber, preserved in vinegar with seasoning, sugar spices and herbs (often dill), but it doesn't have to be a cucumber. In Britain, for example, a 'pickle' is more likely to be a pickled onion. As an uncountable noun, 'pickle' is a condiment made from chopped vegetables in a sweet vinegary relish. Kimchi is a Korean word, and it is very specific. It refers only to the Korean fermented vegetable dish of that name. If you want to explain what it is to an English speaker, you could say that it is a type of pickle.

"A pickle", used as a noun, refers specifically to pickled cucumbers. If we want to describe other kinds of pickled goods, we use the adjective "pickled" as in "Pickled onions" or "Pickled tomatoes" Kimchi refers specifically to Korean pickled/fermented vegetables.