When some of the scholars, such as the Shaykh al-Islam for example, mention that

The questioner : Praise be to Allah, Lord of the worlds, and may peace and blessings be upon the master of the messengers, our Prophet Muhammad (peace and blessings be upon him), and upon all his Companions. If some of the scholars, such as Shaykh al-Islam Ibn Taymiyyah, mention something and it is found in the Sahih, and after research it turns out to be in Sahih Muslim or in Sahih al-Bukhari, is this a term that Shaykh al-Islam preceded to, where one says "the Sahih" meaning al-Bukhari or Muslim?

The Shaykh : Yes, this is not specific to Shaykh al-Islam. The known usage of this term among them is that the one who uses it resorts to it when his memory does not help him to determine the source to which he attributes the hadith, whether it is in Sahih al-Bukhari or in Sahih Muslim. So the matter is taken for granted and he says "it came in the Sahih," meaning in one of them, without any specific designation. This is their intention. There is another technical term that is sometimes intended, either deliberately or by mistake, by "the Sahih," meaning the authentic hadith, without intending by it one of the two Sahihs. That is, "it came in the authentic hadith" is intended first in the previous sense, meaning in one of the two Sahihs, and sometimes it is intended to mean "it came in the Sahih," i.e., in the authentic hadith, without the speaker intending one of the two Sahihs.