Разница в том, что .form-inline позволяет выровнять метки в линию с соответствующими входами..form-inline должен применяться к элементу form.Когда вы используете .d-inline-block, примененный к form-groups, вы можете выровнять их в ряд, но надписи останутся наверху.Проверьте фрагмент ниже, чтобы увидеть разницу:
form {
border: 2px solid black;
padding: 10px;
margin: 10px;
}
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/4.1.0/css/bootstrap.min.css">
<script src="https://ajax.googleapis.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/popper.js/1.14.0/umd/popper.min.js"></script>
<script src="https://maxcdn.bootstrapcdn.com/bootstrap/4.1.0/js/bootstrap.min.js"></script>
<link rel="stylesheet" href="https://use.fontawesome.com/releases/v5.0.13/css/all.css" integrity="sha384-DNOHZ68U8hZfKXOrtjWvjxusGo9WQnrNx2sqG0tfsghAvtVlRW3tvkXWZh58N9jp" crossorigin="anonymous">
<style>
body {
padding: 0px;
margin: 0px;
}
</style>
</head>
<body>
<h6>Inline form</h6>
<form class="form-inline">
<div class="form-group">
<label for="exampleInputEmail1">Email address</label>
<input type="email" class="form-control" id="exampleInputEmail1" aria-describedby="emailHelp" placeholder="Enter email">
</div>
<div class="form-group">
<label for="exampleInputPassword1">Password</label>
<input type="password" class="form-control" id="exampleInputPassword1" placeholder="Password">
</div>
<div class="form-group d-inline-block">
<button type="submit" class="btn btn-success ml-3">Login</button>
<button type="submit" class="btn btn-primary">Login with facebook</button>
</div>
</form>
<h6>Not inline form with .form-group.d-inline-block</h6>
<form>
<div class="form-group d-inline-block">
<label for="exampleInputEmail1">Email address</label>
<input type="email" class="form-control" id="exampleInputEmail1" aria-describedby="emailHelp" placeholder="Enter email">
</div>
<div class="form-group d-inline-block">
<label for="exampleInputPassword1">Password</label>
<input type="password" class="form-control" id="exampleInputPassword1" placeholder="Password">
</div>
<div class="form-group d-inline-block">
<button type="submit" class="btn btn-success ml-3">Login</button>
<button type="submit" class="btn btn-primary">Login with facebook</button>
</div>
</form>
</body>
</html>