Nationally, there is some variation in how the term "internship" and "externship." So, to be sure, you have to ask the particular hospital offering the program.
But as UVA Grad Nursing said, the term "externship" usually refers to a job for people who are still in nursing school
-- prior to graduation. In some places, it is just a glorified tech or CNA position. In other places, externships provide a more formalized education program designed to supplenment the studen extern's formal education in school.
The word "internship" is usually used to refer to an extensive orientation program designed with new grads in mind -- but may also be used by experienced nurses switching specialties. Another word for such programs is "residency."
Some hospitals use the word "internship" for their student jobs -- and/or simply use the expression "new grad orientation" to describe a special program for new grads. That's why you have to clarify with each hospital exactly what THEIR hospital means by the words they choose and what exactly involved in any special programs offered.
Also remember that the quality of a program is more important than the word chosen to name it. Just because a hospital uses a special word and/or has a pretty brochure and other good marketing materials ... doesn't guarantee that the program is of good quality. There are many wonderful student programs and new grad oriention programs that don't use any special labels or have fancy marketing materials. They rely on their excellent reputation and word-of-mouth for recruiting and don't need to spend money on a lot of expensive marketing strategies. There are also some programs with fancy marketing materials that are of poor quality. That's why they have to spend more of their resources on their marketing materials.