Harvey,
PayPal is payment processor (third party), and Moodle lets you use your PayPal account to take payments for courses which eventually goes to your PayPal. So user taking course with PayPal symbol, must make payment via their PayPal to take the course, and with pre-set criteria (like Payment is monthly or weekly), once Payment expires, user's enrollment automatically cancels.
Self Enrollment is like, users can self enroll in the course, either by clicking enroll me in this course, or by using the pre-shared enrollment key that course creator can give to prospected students.
Other method is manual enrollment which is opposite to self enrollment, in manual enrollment only course creator assigns users to the course, users dont have ability to self enroll.
so courses that show PayPal + Self Enroll, means users can self enroll in the course, but they have to make payment before they can actually take the course.
PayPal + NO Self Enroll means, users are allocated courses only by course creator, but, to take that course they have to make payment through PayPal.
as per showing either is concerned, it all depends on how your teaching methodology works, You may be registering students on session basis or site is open to take course at anytime by anyone.
if its session/semester system teaching, then you dont have to keep self enroll ON, as users will be assigned courses and at the end of the session/semester, they will leave the course/sent out manually.
if its open site to take course anytime by any registered user, then self enrollment has to be turned on so site users can come and take course they like anytime.
if you are not taking payment separately before session start, then PayPal will let you take payments online as well at the time of someone taking the course. if you are taking fee for the course prior to session start, then you can turn off the PayPal option.
hope I have made you confused, if you still cannot understand, let me know, I will use case scenario of a University or something.