As explained to Movie Pilot by Warwick Davis himself,
When it came to the third film, of course the looks of the whole films had changed.
Alfonso really wanted to put his mark on the films. And then a lot of things altered: anything from character looks, to the actual layout of Hogwarts itself.
And another thing was happening at the same time. There wasn't really anything for Flitwick in the script at all, and I got a call one day from the producer, saying basically, "There's nothing for you, but we'd love you to be in the film all the same. How do you fancy coming in and doing a kind of cameo in the film as somebody else?"
And I said, "Well, that's great, thanks for asking. I'm always thrilled to be part of all of this, anyway." So, I went in for a meeting with Alfonso, the director, and Nick Dougland, who's the make-up supervisor, and we came up with this new look for this character who would be basically the conductor of the Frog Chorus in the Great Hall. And so, we went with that.
Are they the same person?
There's been debate over whether the original Flitwick and the younger, grumpier choir master are the same character, but they are confirmed as the same character more than once, most obviously when McGonagall addresses him as 'Filius' in Deathly Hallows II.
Someone asked actor Warwick Davis on Twitter as mentioned on this article, though I couldn't find that tweet.
Could you possibly give us an insight as to why Flitwick's look was changed for the third HP movie?
So many of you have asked me the 'New look Flitwick' question, so I will answer it here, once and for all. When it came time to shoot 'Azkaban', there was no mention of 'Flitwick'' in the script. However, the producer still wanted me to be in the movie, so he asked if I would play the role of 'Choir Master'. Of course, I said 'yes'. When it came time to shoot 'Goblet of Fire', the director, Michael Newell said he liked the look of the choir master, and from that moment, the character became known as 'Flitwick'.
There was no role for Flitwick in the film adaptation of Harry Potter and the Prisoner of Azkaban; but he was offered a small part as the conductor of the Hogwarts chorus who appeared as a small man with brown hair and mustache.
Now coming to your questions.
Is this only limited to movies or the same in the books?
AFAIK, this change was limited to movies only.
Why did this change happen? Is the reason explained by J.K Rowling or the directors of the movies?
Apparently, Michael Newell liked the look of the choir master, and since then, the character became known as Flitwick.