If I understand you correctly, I think there is the same purpose for any FS design choices. For example, I saw both approaches data store and declarative feature computation on demand.

An important part for product is basically support of 2 features:
feature retrieval for a batch of entities (useful for generating training sets together with ability to do time travel; batch prediction (offline) ); feature serving in near real-time (online).
This is minimum functionality I would expect a feature store do on a lower level. However, there are more purpose on it for feature reuse, governance and declarative feature engineering, so data scientists could focus on what data they need instead of how to get it.

There are plenty of good materials about it on http://featurestore.org .