They are not the same, however Eloquent collections extend the base Laravel collection object, thus inheriting all the methods provided by the base collection.
When retrieving a record from a table using Eloquent ORM, the resulting object is an Eloquent collection. So you can use Laravel collection methods on Eloquent collections.
In addition, what you should note is that an Eloquent model is a query builder thus all the methods available in the Query Builder may be used in Eloquent queries and then the get() method is used to retrieve the results as an Eloquent collection.
$user = App\User::whereNotNull('email_verified_at')
->orderBy('id', 'desc')
->take(20)
->get();
EDIT:
When retrieving a record from a table using Eloquent ORM, the resulting object is an Eloquent collection. So you can use Laravel collection methods on Eloquent collections.
When retrieving a single record from a table using Eloquent ORM (first(), find(), firstOrFail() and findOrFail()) the resulting object is a model. However, all multi-result sets returned by Eloquent are Laravel collection objects - instances of Illuminate\Database\Eloquent\Collection, including results retrieved via the get() method or accessed via a relationship. So you can use Laravel collection methods on Eloquent collections.