Key differences between interactive and time sharing operating systems?
Time sharing is a system of multi-tasking designed to allow multiple users to use a single machine at the same time.
A time sharing operating system is one that supports multi-tasking and multi-user.
In a time-sharing system the user typically interacts with the operating system through a secondary machine called a terminal.   

In an interactive operating system there is typically only one user on the system that has full control over the system.

Because of the environment in which time-sharing machines are used (large cooperations and banks) security and separation between users is a prime concern.  

Interactive computing originates from the hobby and personal computing revolution. Because there is only a single user security was initially not a concern.  

From these starting points the lines have blurred.
First single user systems gained multi-tasking and then multi-user concepts were copied over from time-sharing systems into the interactive OS'es.  

Meanwhile the security and performance of time sharing systems have also improved.