Hi,
I completely understand your initial confusion. We have tried to clear this out with the diagram.
So, if you take a look at the diagram provided in the  ‘Intro to data science’ course, you will see that for the most part data science and data analytics overlap.
This means that often times the same activities can be classified as both data science and data analytics.
On some occasions we might me using data analytics but not data science. For example, companies use digital signal to represent data in the form of discrete values. They apply data analytics to digital signal to produce a higher quality signal, without going into data science.
Hope this helps!