For the moment (Django 1.9 and earlier), {% load staticfiles %} loads the static templatetag from the contrib app that has more features than the built-in django.core.static.
The most important difference is staticfiles can manage files stored on CDN, since its resolver can manage hashes for example. core.static only append STATIC_URL to the static filename, which is not enough if you're processing your files (e.g. adding md5 hash to clear cache between releases)
This difference is due to the fact that managing non-local storage files was not dedicated to be included in the core package of Django, but was still useful to many developers to be implemented as a official contrib package. So if you started to use staticfiles, you had to remember to use it every in your templates. BUT, some problems could appear, for example when using Media classes so the decision has been to merge those two templatetags into one and use a different behaviour whether the developer has django.contrib.staticfiles in its INSTALLED_APPS or not.
From Django 1.10 and onwards (also see ticket in Django tracker), the {% load static %} is going to use staticfiles internally if activated (oherwise keep default behaviour), and the templatetag in the contrib package will be deprecated to avoid confusion. 
TL;DR
- Before Django 1.10: staticfilesloads a templatetags that can manage non-local storage wherestaticcan't (or not easily) ;
- From Django 1.10: contrib.staticfilesapp still exist but its templatetags will be removed only the{% static %}templatetags remains ;
- From Django 2.0 (I believe): {% load staticfiles %}is removed.
For now, use staticfiles templatetags if you use the related contrib app (and you know why you are using it) until Django 1.10, otherwise just use static.