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Can someone give me an example each where these two tools would be appropriate to use. I kind of understood what each of them does but can't seem to figure out examples where one would be more appropriate than the other. Both seem to show density just fine.

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I believe it depends on what you want to analyze to determine which tool will suit your needs. Both tools smooth out the information represented by a collection of points in a way that is pleasing visually. The purpose of the point and Kernal Density tools is to attempt to construct a surface that perfectly reflects the likelihood of an event. Point density calculates a magnitude per unit area from point features that fall within a neighborhood around each cell. KD calculates the density of features in a neighborhood around those features. i.e., finding density of houses, or crime reports influencing a city. Point density calculates a magnitude per unit area from point features. KD instead spreads the known quantity of the population for each point out from the point location. A kernal function is then used to fit a smoothly tapered surface to each point. https://blogs.esri.com/esri/arcgis/2013/05/28/how-should-i-interpret-the-output-of-density-tools/

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