both of them are the same exact thing developed and maintained by pretty much same exact people (see contributors). the difference is that it is worked on under bitcoin-core github account and in a separate repository and the stable versions are pulled to bitcoin account in bitcoin/bitcoin repository.

the benefit is that if a developer wanted to use libsecp256k1 in their project they don't have to download the much bigger project (bitcoin core) and extract the libsecp256k1 from it. they can easily download a standalone repository and compile that without having to remove the extra parts (bitcoin core related parts).