It is permissible to describe a specific person as a believer if what is meant is their outward Islam and the application of the rulings of Islam to them. However, testifying that a particular individual possesses complete faith that deserves praise, commendation, and Paradise cannot be stated with certainty except for those whom the Qur'an or the Sunnah has explicitly testified to. In this way, the apparent contradiction between the two hadiths is resolved.
The answer requires some detail because the term faith (Iman) is used in the Islamic texts with two different meanings.
This refers to outward Islam, whose signs appear through the testimony of faith and the visible rulings of Islam.
Whoever is outwardly established as a Muslim may be described as a believer in this sense, and the rulings that apply to believers in this worldly life apply to him.
Examples include:
This refers to the inward faith whose true reality is known only to Allah. It is this faith that leads to complete reward and entry into Paradise.
No one may definitively testify that a particular individual possesses this level of faith unless revelation has explicitly testified to it or there is a clear textual proof.
When the Prophet ﷺ asked the slave girl about her Lord and about his prophethood, her outward Islam became evident to him.
Therefore, he said:
"Free her, for she is a believer."
That is, she was a believer in the sense that the outward rulings of Islam applied to her.
The Prophet ﷺ was not making a definitive judgment regarding the true reality of the faith hidden within her heart.
Sa'd said about a certain man:
"I consider him to be a believer."
The Prophet ﷺ replied:
"Or rather, a Muslim."
This was because Sa'd had moved from judging by outward appearance to making an implicit judgment about the man's inward faith.
The Prophet ﷺ therefore directed him to limit his statement to what could be known with certainty—namely, the person's outward Islam.
The scholars explained that people are divided into levels in this regard:
A person may outwardly be a Muslim while the true level of his inward faith remains known only to Allah.
For this reason, the early righteous generations were careful not to praise individuals by affirming complete faith for them without evidence.
This is permissible in two situations:
One may say:
Meaning that he belongs to the Muslim community and the rulings of Islam apply to him.
This cannot be affirmed with certainty except for those whom the Qur'an or the Sunnah has explicitly testified to, such as:
And Allah knows best.