Shaykh Ibn Uthaymeen explains that anyone who follows the way of the Prophet (sallallaahu alayhi wasallam) and his Companions is a Salafi and that ony the Salafis who adhere to the way of the Salaf (in truth) are Ahl al-Sunnah wal-Jamaa'ah:

قال العلامة الشيخ محمد بن صالح العثيمين رحمه الله تعالى : فأهل السنة والجماعة هم السلف معتقداً حتى المتأخر إلى يوم القيامة إذا كان على طريق النبي صلى الله عليه وسلم وأصحابه فإنه سلفي

The Allaamah, Shaykh Muhammad bin Saalih al-Uthaymeen (rahimahullaah) said (Sharh al-Aqeedah al-Waasitiyyah 1/45):

For Ahl al-Sunnah wal-Jamaa'ah, they are the Salaf in terms of creed, even the latecomer until the Day of Judgement, if he is upon the way of the Prophet (sallallaahu alayhi wasallam) and his Companions then he is a Salafi.

And in the first cassette of his explanation of al-Aqeedah al-Safaraaniyyah, he said:

من هم أهل الأثر ؟ هم الذين اتبعوا الأثار ، اتبعوا الكتاب والسنة وأقوال الصحابة رضي الله عنهم وهذا لا يتأتى في أي فرقة من الفرق إلا على السلفيين الذين التزموا طريق السلف

Who are the Ahl al-Athar? They are the ones who follow the aathaar (narrations), they follow the Book and the Sunnah and the sayings of the Companions (radiallaahu anhum). And this does not stem (arise) from anyone sect from the sects except the Salafis, those who cling to the way of the Salaf.

Shaykh Ibn al-Uthaymeen (rahimahullaah) has some other speech in which he warns that Salafiyyah is not a "hizb" (a party amongst the parties) but that it is following the way of the Salaf truthfully, we shall document that separately and answer many of the doubts of the biased partisans who used that speech in order to attack ascription to the Salaf in ones creed and methodology.