BBC,
"She (Theresa May) has insisted that no EU national currently resident in the UK would have to leave at the point of Brexit and that people will be treated the same irrespective of their nationality.
The main feature is the offer of "settled status" for EU citizens, as well of nationals of Norway, Iceland, Liechtenstein and Switzerland, who have been living legally and continuously in the UK for at least five years"

https://www.bbc.co.uk/news/uk-politics-40379663

Yes they will have to apply for it, but all EU citizens qualify.
No such reassurance has been offerd to UK citizens in EU. Nothing for them to apply for.