Eeesh. That’s quite the challenge. If you avoid chemistry definitions, you can really only get a very basic understanding of what those terms mean.
I think the pivotal concept that cannot be avoided would be “charge” (or “electrical charge” but for simplicity’s sake, lets stick with “charge” for now). A molecule can either have a “charge” or not have a “charge”. If it does have a “charge” it is said to be “ionic“, and conversely if it does not have a “charge” it is said to be “non-ionic“.
Now within this broad definition of “charge” we are working with, there are two kinds. “Positive charge” and “negative charge”. If a molecule has a “positive charge” it is said to be “Cationic“. If a molecule has a “negative charge” it is said to be “Anionic“.