Is there a difference between potato starch and potato flour? Corn starch is made from the endosperm of the corn kernel does this also apply to potato starch? I have tried both and I cannot really taste or feel a difference
In principle, there is a difference, yes. I'm not sure how it relates to products and their labeling, though.
Starch is, strictly speaking, a chemical compound. It is produced by different plants, and you can isolate it from them.
Flour is a fine powder made of dried plants - the prototypical case is wheat, but the word covers easily all of the grain and pseudograin flours, and it's also used for other high-starch powders such as potato, plantatain or chestnut flour. It contains not only starch, but also the cell walls and other non-water stuff found in the plant's cells.
Admittedly, flours are made from plant parts which are specialized to store starch, so there would be very few non-starch components in potato flour. So I don't think that you'd notice the difference between pure extracted potato starch and milled potato flour in daily use. I tend to use the same product whatever the recipe says (here in Germany, it's sold as potato flour, Kartoffelmehl) and haven't had anything fail.
I've seen books though which make a point to use one and not the other. These are usually books on gluten-free baking, where the authors spend hours perfecting a mix of different starches and flours to get a good result. For example, see Carol Kicinsky's all-purpose flour blend: she warns both to use potato starch and not potato flour, and to not use a specific brand of potato starch, "as it is made with sweet potatoes and is not the same".
I have never researched labeling requirements for potato starch and potato flour, and these may well vary by jurisdiction. If sweet potato starch is allowed to be labeled as potato starch, I wouldn't be surprised if it's also the case that producers are allowed to mill a potato flour without doing any extractions, and label the result as "potato starch", since it's mostly starch anyway. But I have no idea if this is legally allowed or not.
To sum it up: for everyday purposes, if you just need a generic kind of starch, you can use potato starch and potato flour interchangeably (and other similar types of starch too). If you suspect that the recipe has low tolerances, stick to the letter and use exactly what it prescribes.
If they are correctly labeled, they are not the same thing, and can only be substituted in certain recipes.
Potato starch is the dried pure starch was washed out of potatoes. Potato flour is 100% of the potato flesh, dried and then ground into fine meal. Per King Arthur flours:
What’s the difference? Potato flour includes fiber, protein, and flavor, while potato starch is pure flavorless starch.
This means that potato starch will not work as a substitute for potato flour if you are making a bread which expects the flour to have "substance". Likewise, if you are making Korean dumplings that expect pure colorless potato starch, you cannot use potato flour instead.
Of course, there will be another set of recipes where it genuinely doesn't matter, particularly ones where you are adding small amounts of flour/starch as a thickener. Additionally, if a product is multi-lingually labeled, potato starch sometimes gets labeled as potato flour and vice-versa. So you should check the ingredients in whatever you're buying.
Just for additional reference and clarity, here are some technical documentation for your review:
Product: Potato Starch (clean label)
Specification Sheet: [Original Not Available] [Backup]
Additionally, there is a technical whitepaper published by Potatoes USA that is intended for the cracker manufacturing sector; it is very detailed, and has a section that covers the functional differences between the flours and starches in-depth. Here is the whitepaper and a backup.