The first line of code -
public SomeListViewModel SearchSomeModel => new ShowSomeViewModel{...};
means that it will create a new instance of ShowSomeViewModel every time that you try to get it.
It is the equivalent of:
public SomeListViewModel SearchSomeModel {
get {return new ShowSomeViewModel{...};}
}
On the other hand the
public SomeListViewModel SearchSomeModel {get;} = new ShowSomeViewModel{...};
means you are setting a default value.