There are only a handful of texts that can be termed classical Vedic Upanishads, as they form part of a Vedic text such as a Samhita, a Brahmana or an Aranyaka. Some of these are recognized as having been part of a Veda shakha that is lost now, and only the Upanishad has survived. This can be deduced from the linguistic elements and the subject matter of them.
Accordingly, the Vedic Upanishads that at least Adi Shankara has written commentaries on are enumerated in this shloka:
ईश केन कठा प्रश्न मुण्ड माण्डूक्य तैत्तिरी । ऐतरेयं च छान्दोग्यं बृहदारण्यकं दशम् ॥
Isha, Kena, Katha, Prashna, Mundaka, Mandukya, Taittiriya, Aitareya, Chandogya, Brhadaranyaka.
In addition, Kaushitaki, Mahanarayana, and Shvetashvatara are also Vedic Upanishads.
The above texts are distinguishable not only because of their location within a Vedic text, but also by their archaic and ancient Vedic language style, and also by the fact that their subject matter and discussion are classical Vedic in character. The key factor is that they don't stress sannyasa.
All other texts that go under the title of "Upanishad" are just copying the format of the classical texts due to the prestige and renown for the term "Upanishad".
Just as Bhagavad Gita is the original "Gita", but later texts such as Ashtavakra Gita, Uddhava Gita, Manki Gita, Rama Gita, Hanuman Gita, etc. all copied the format of Bhagavad Gita because of the prestige and renown for the term "Gita".