The anime version features an original story, starting with Boruto entering the ninja school (or "Academy").
From Anime News Network,
This year's ninth issue of Shueisha's Weekly Shonen Jump magazine is announcing Monday that the Boruto: Naruto Next Generations television anime will begin with an original story.
(Emphasis mine)
From Japanese Wikipedia,
テレビアニメ化にあたっては、映画や漫画よりも前の時系列にあたる忍者学校でのエピソードが制作され、アニメとノベライズにて描かれている。
Regarding the anime adaptation, it tells the earlier story from the movie and manga about the ninja school, which is shown in the anime and novel.
also,
前述の通り、原作を一から映像化するのではなく、前日譚となる「忍者学校入学編」から始まり、同編の終了後は原作者の岸本が執筆した『NARUTO -ナルト- 外伝〜七代目火影と緋色の花つ月〜』を原作とした「うちはサラダ編」が放送された。第39話では同じく原作者の岸本が執筆した外伝『満ちた月が照らす道』が放送された。
As have been mentioned before, (the anime) doesn't start from the beginning of the manga but starts from the earlier life in "Academy" arc, then continues to "Sarada Uchiha" arc from Naruto Gaiden: The Seventh Hokage and the Scarlet Spring, then "School Trip" arc. Episode 39 also continues to Naruto Gaiden: Michita Tsuki ga Terasu Michi.
As for now, there's no hint if the anime will adapt (retell) the manga/movie's storyline even though recent manga chapters sometimes refer to the anime's plot.
The manga itself starts as an adaptation from the movie (see What is the difference between Boruto: Naruto Next Generation and Boruto: Naruto the Movie).