Both answers here are giving really good definitions of the concepts, but I think it's important to additionally talk about the relation between the two to clarify the justified confusion and to compare them.
tl;dr RER is combining PPP theory with the current exchange rate to produce a rate that is taking purchase power into account. Read the two last paragraph to understand the confusion.
Purchasing Power Parity (PPP) is a theory that measures prices at different locations using a common basket of goods.
PPP is giving us a ratio (rate) that is fair in purchase power between different locations (according to the basket of goods).
The market exchange rates are not following PPP. This is why the RER exists. We apply PPP theory to the current exchange rates to get a "real" rate that takes purchase power into account. In other words, RER is using PPP.
The real exchange rate (RER) is the purchasing power of a currency relative to another at current exchange rates and prices
This is confusing because, at least in online litterature, we don't seem to be explicitly mentioning their relation. For example, when we talk and teach about PPP, we often associate it with simple price indices to give usage examples (e.g. the Big Mac Index). These indices are using the current exchange rate to compare between countries, so they are simply RERs normalized to one currency and using a specific good basket for the comparison (in this case one single item, the Big Mac). Since this is not mentionned and one leads to the other, the distinction often becomes unclear.
Another confusion factor is that you can easily find PPP rates, exchange rates and price indices online, but not RERs.