When Arabic-speaking Muslims perform صلاة/ṣalāt, Persianate Muslims do نماز/namāz – or actually, ‘read’ namāz. Among Chinese-speaking Muslims (Hui, or Dungan), most of whom share the same ancestors as modern Tajiks, the Islamic prayer is 乃玛孜/nǎimǎzī (sometimes also 乃麻子／nǎimázi), evidently a transliteration of نماز/namāz.
Many are familiar with the term نماز/namāz and the Hindi/Sanskrit greeting नमस्ते/namaste separately, but have never realised that they are, in fact, the same word, and essentially, the same concept.
नमस्ते/namaste is in reality two words, namas and te, where namas means ‘bow’, therefore ‘reverence’, and therefore ‘adoration, homage, veneration’, and te is the second person dative singular of the personal pronoun त्वम्/tvam ‘you’. Therefore नमस्ते/namaste actually means ‘bow to you’ or ‘reverence to you’ – a meaning that is only transparent in Sanskrit and obscured in Hindi.
The Persian نماز/namāz is the same word as the Sanskrit word above, and used to mean exactly the same thing. Both come from the Indo-Iranian verbal root *nam- ‘to bend, to bow’, which came from the Proto-Indo-European *nem, with the same meaning. Natively in Iranian, the Kurmanji word for ‘prayer’ is nimêj, where the ê reflects a regular sound change from SW Iranian to NW Iranian, and the j recalls Parthian, where the word was namāč. Cheung (2007) points out that the Kurdish dā nawin (<*namin) and the Awromani (ara-)nāmiāy/nāmia- both mean ‘to bend down’, so the root is somehow still alive in New Iranian.
So when one performs نماز/namāz, semantically one is saying नमस्ते/namaste to God. In fact, the root *nam- includes the sense of prostration, as a prostration is an exaggerated form of a bow, and both involve bending one’s body.
As I mentioned, the verb that collocates with نماز/namāz, in many Persianate languages, is the verb ‘to read’. In Persian, it is خواندن/kh(w)āndan , in Turkic, oQu- (Azerbaijani oxu-, Uzbek o‘qi-, Uyghur ئوقۇ-/oqu-, etc.), and in Urdu, پڑھنا/paṛhnā. Modern standard Turkish, however, uses the verb kıl- (<OTr qil- ‘to do’), and so does Kurmanji (kirin, ‘to do’). Interestingly, Russian-speaking Muslims also use the verb читать/chitat’, ‘to read’, most certainly a calque from the native languages of the Muslims the Russians colonised.
Furthermore, the Buddhist devotional expression, namo Amitābha (in Chinese, 南无阿弥陀佛／nánwú (in earlier pronunciation, námmó) ēmītuófó) also contains the word. Namo is the sandhi form of the Sanskrit नमस्/namas in the nominative singular, and also the actual nominative singular form of the same word in Avestan. Thus, when Buddhists pay homage to the deity Amitābha with this phrase, they are actually performing نماز/namāz, too. Many Zoroastrian expressions of veneration also start with namō, the surface form of nama- in Avestan (*-s being the nominative singular ending in Indo-Iranian).
The Hindi/Sanskrit greeting नमस्कार/namaskār(as) could actually have a New Persian equivalent that makes perfect sense – نمازکار/namāzkār, which designates the ‘doer of namāz‘. Now imagine if that was a greeting in modern Persian…