Let me try:
1. Feature service is 'feature accessible' map service published on ArcGIS Server site.
The source of your data has to be a database.
2. While hosted feature layer is spatial data published to ArcGIS Online or Portal for ArcGIS.
The source of your data can be:
BTW, of course you can publish your data from database through SDE connection by ArcGIS Desktop.
Adding to the comment above:
Feel free to reach out if you have additional questions or concerns!
This presentation may also help explain these two terms in more detail: Best Practices for Layers and Service Types - YouTube (see from around 2:25 and a few minutes onwards).
Using the concepts from that presentation a feature service is the raw web service (REST) endpoint found at the functional or GIS Server tier. The feature layer is an item found at the information model or portal tier and sits on top of the raw feature service itself and provides additional features and control.
The two terms are often used a bit imprecisely as synonyms. For the most part the distinction doesn't matter too much but when developing or troubleshooting it can be important to distinguish and understand the difference.
One way that I look at it this:
|When source is a feature service||When source is a map service|