Le Cèdre Bellevue is the young brother of Le Cèdre at Badenerstrasse (see the Le Cedre article). It opened in April this year, apparently to fill in some gaps that the original venue left open. It is managed by the (younger?) brother of the charmeur who rules the place in Badenerstrasse.
The difference between the two restaurants can be best summarized in two words: location and occasion.
About the location: the new restaurant is located more near the city center, the river and the lake. Most importantly, it has a big terrace.
For which occasion(s)? Here are some examples: a lunch if you are working in the area or visiting Zurich, an outdoors dinner during a warm evening, a snack for reacting to hunger after a swim nearby. So if the original place is ideal for a special experience, to be planned and savored in each detail, the new venue is mostly chosen after spontaneous decision-making.
The menu at Cèdre Bellevue is a subset of the menu of the original restaurant. However, if you are a regular of Badenerstrasse and don’t see your favorites in the menu, just ask. I myself realized that the Viagra (name of an appetizer, Pfizer is not directly contributing to its preparation) was available although it was not listed.