She had a closet full of them.

@Background Pony #2CEE  
Yeah, generally speaking it doesn’t have to be about the item as much as the memories.  
The disc-world dwarves I felt had the best approach to sentimental attachment: When an axe is passed down through the family, sometimes it needs a new head, other times they need to replace the handle, but it’s still the same axe.  
While AJ replaced it all at once, it’s still visibly identical, AND she has that closet full, so it’s ‘the same hat’.
 
Others might say things like ‘I feel naked without a wristwatch’, but over the years the watches haven’t even been visibly similar, just sharing the fact they are wrist-worn and tell time.

why does applejack’s hat have a tag… it doesn’t make sense at all XD

Yeah, she lost that hat, but I doubt it meant all that much- remember, the Apples have an entire closet specifically dedicated to hats and bows.