Since their first appearance in 1963, the Avengers had been headquartered in Avengers Mansion, which was originally Tony Stark's family home. However, the Mansion was destroyed in Avengers Disassembled, so in New Avengers (2005), the Avengers moved into Stark Tower, alternatively known as Avengers Tower.
Later on, Stark Tower would be rebuilt at various times, which changed its appearance each time:
Stark Tower would also appear in The Avengers (2012), with the A in "Stark" cleverly becoming the Avengers A after the rest of the sign is damaged in the Battle of New York. However, this Stark Tower looked quite different.
Yet, despite the very distinctive appearance that pretty much everyone on the planet is familiar with, Marvel kept the design of Stark Tower they were already using. It would show up every now and then, and I can only guess to reasons why, but it would never stick. For instance, here it is in A+X #2 (November 2012), where it represents Resilient's headquarters, which could be Stark Tower or a separate building entirely:
However, during the eight month gap Secret Wars took place during, Tony Stark had to sell off Stark Tower, and in All-New, All-Different Avengers #1 (October 2015) where we learn this, it is clearly based on the movie version:
As it appears this way in another All-New, All-Different Marvel book as well, I can only assume the restructuring of Universe 7 into Universe 8 (see The Ultimates (2015) for more information) caused some MCU stuff to seep through.