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Description

The clues are there.

safe2212220 edit176973 edited screencap93247 screencap298939 apple bloom60913 big macintosh34167 goldie delicious455 pinkie pie259964 earth pony521233 pony1642356 g42066810 hearth's warming eve (episode)802 pinkie apple pie1116 book44612 comparison5369 dust cat7 female1846455 filly100742 gingerbread house116 hearth's warming eve1661 image macro40358 in which pinkie pie forgets how to gravity163 jenga71 male565564 mare768592 meme95202 pinkie being pinkie1756 pinkie physics547 scroll4415 stallion202392
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Background Pony #B9EA
There is also the greeting.
 
Pinkie pie: “Ahhh yourself” beginning of the episode  
Goldie delicious: “Hello yourself”
A Sad Pony
Artist -
The End wasn't The End - Found a new home after the great exodus of 2012

I made a .gif once
All in all, it’s still ambiguous. Perhaps Goldie Delicious herself was simply a zany, Pinkie-like Apple in her youth. She’s certainly eccentric.
 
Dunno. Maybe this’ll tie in later.
Background Pony Number 17
My Little Pony - 1992 Edition

@Hellfire  
Pinkie Pie said she was a fourth cousin twice removed by a fifth cousin. That’s so distant, considering the size of the Apple Family, that half the Earth ponies of Equestria could claim the same thing. Certainly nearly all of the ones around Ponyville could–it’s not that big of a town for its families not to be related somehow.
 
That said, there’s definitely some kind of a connection between Goldie Delicious and Pinkie Pie going on here.
Hellfire
The End wasn't The End - Found a new home after the great exodus of 2012

I didn’t think it was very farfetched. Any couple of families liking in the same region for several generations are likely to be connected somewhere.
F

Applejack related to the Pies or Pinkie Pie related to the Apples, does that make any big difference?  
Both families are related in both cases.
Background Pony #75C9
!s3-live.tapcdn.com/images/tap/b/4/0/3/c/257/be9/400-animate/google-image-result-for-http-cupofzup-com-wp-content-uploads-2012-04-mother-of-god-gif.gif!