What are the day to day responsibilities of the 2 roles and how much do they differ.
As a data scientist I am not sure of the answer to that question lol. I do create train models and ship them to production. Mostly my customer is other msft teams. I am not sure how it's different then applied scientist. Having said that one weak pattern i saw is that most of the time data scientist looks at the data creates models and give insights does experiements and all that but usually does not create the prod product. But applied scientist people they go ahead and write the actual production code. This might be completely wrong so full disclosure. Source: dude, trust me.
Applied researchers work with SDEs for making production code, but they don't actually write it. It is not expected that the applied researchers will know how to write production code themselves. Source: I'm a SDE manager at MSR.
So, how is applied scientist differ from data scientist?
They are the same job family. But generally ML people prefer to identify themselves as applied scientist. Data scientist these days refer to analytics and BI.
True in a way they are data analysts that effectively leverage ML and DL algorithms and use advance techniques that requires some coding knowledge. Nonetheless they are essential to a product since they wont favor the model and premature ship a product. Instead they will stay true to the data and the numbers they have and try to postpone or give honest feedback to the ship decision making people.