When you go to a Hosted Feature Service's Settings (Overview) page, you have the option to "Create View Layer". I'm familiar with the concept and I understand what's going on here.
However, on the Visualization tab you also have the option to "Save As New Layer". What is the difference between doing this (aside from the option to save a single layer?) and creating a view?
Based on Create hosted feature layer views—ArcGIS Online Help | Documentation I'm taking a guess that you have more granular control over a HFS View as compared to the New Layer option. Am I missing anything else?
The description in "My Content" is different also.