A List<string> is a concrete implementation of IEnumerable<string>. The difference is that IEnumerable<string> is merely a sequence of string but a List<string> is indexable by an int index, can be added to and removed from and have items inserted at a particular index.
Basically, the interface IEnumerable<string> lets you stream the string in the sequence but List<string> lets you do this as well as modify and access the items in the lists in specific ways. An IEnumerable<string> is general sequence of string that can be iterated but doesn’t allow random access. A List<string> is a specific random-access variable-size collection.