One is for Procedural style programming and other is for OOP style programming. Both serve the same purpose; Open a new connection to the MySQL server
OOP Style usage
$mysqli = new mysqli('localhost', 'my_user', 'my_password', 'my_db');
Procedural Style usage
$link = mysqli_connect('localhost', 'my_user', 'my_password', 'my_db');
Reference: PHP Manual
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