Quite a lot! Here are some of the main ones.
C# connects to the .NET framework, providing easy, efficient access to libraries containing many commonly-used classes. However, although it’s possible to use purely open-source C# for everything, it’s difficult. At some point the likelihood is that you’ll be pushed into paying for Microsoft tools to keep using C#.
Swift, on the other hand, allows access to a less broad array of third-party tools, but is currently and will remain fully open-source. Note that it is a language fully designed and controlled by Apple, and that open-source does not necessarily mean an open contribution process.
Although principally object-oriented, C# also supports certain features of functional languages, for instance lambdas and anonymous classes.
The Swift codebase is concise, clear and quite close to spoken English, making it easy to pick up. It’s also extremely fast and efficient to run as a compiled language vs. C# which is an interpreted language (hence its name).
C# is used for Windows programs, while Swift was designed entirely for use on Apple machines (iOS and MacOS).
Apparently it is possible to build iOS apps with C#, through Xamarin. I haven’t tried this so can’t speak for its success rates. While it’s possible to run Swift code in other environments, I haven’t ever seen serious usage of that.
C# is at a great time in its life cycle—it’s been around for a long time so there are many people who are very familiar with it. It is regularly updated, versatile, easy to read and write and has excellent tooling support. It’s the go-to language for many organisations, and due to its broad range of capabilities, will remain popular for a while to come.
Swift is newer, and still prone to updates that may change the way you write your code. Fewer people know it, so there are fewer resources to ask questions of.
Finally, C# is also used a lot in gaming and VR work. If games are your thing, Unity engineers prefer C#, so you’ll be positioning yourself really well to work with arguably the top player in the industry.
These are the ones I can think of off the top of my head. I’m sure there are other differences too, but hopefully this answers your question for now.