What does it mean when apps claim they encrypt at REST and HTTPS? I find this a little difficult to understand how different they are from the rest of the encryption-based Apps.
HTTPS is one form of "encryption in transit", which means that data passing over the network to or from the application is encrypted. "Encryption at rest" means that the data the application stores on its local storage is encrypted, so that an attacker who can access the storage but not the application itself can’t read the data.
HTTPS a protocol with which an application can communicate securely with a backend service, such as a database. It is the encrypted companion of another protocol, called HTTP. You've most likely seen those 2 protocols being used if you've ever used a web-browser on a Desktop machine.
When an application claims that it's using HTTPS, it's telling you that information you provide is transmitted using a secure, encrypted connection. This is especially important for sensitive tasks, such as credit card transactions, where a potential badguy otherwise would be able to eavesdrop and steal your creditcard information.
Thus HTTPS provides you with encryption in transit which leaves us to the next part.
encryption at rest is a term used by applications to notify you that they employ some sort of encryption scheme to protect the data that they store. Building on the example above, once your credit card transaction is complete, the app might ask you if they should save the provided information to make the next purchase quicker (I'm not quite sure that's okay if you want to stay PCI compliant, but bear with me here). If you agree, and the application claims to use encryption at rest, then you can be pretty sure that they encrypt the stored credit card details.
Please do remember that using encryption at rest does not mean that everything is encrypted. It also doesn't mean that the encryption in use is of sound design or is safe to use. Look for information where they specifically state what algorithms and ciphermodes being used. If they're willing to part with that information, you can be pretty sure they know what they are doing.