Samā' (Arabic: سماء) is what is opposite of Earth and elevated from it, and may include the space in between. It is typically used to mean sky in English and may be used to refer a tangible thing (firmament).
According to Islamic belief, there are seven skies, each one engulfing the one preceding it (concentrically, if you wish, assuming that the skies have uniform geometrical shapes and that there is a center to such structure, of which we have no textual evidence):
هُوَ الَّذِي خَلَقَ لَكُم مَّا فِي الْأَرْضِ جَمِيعًا ثُمَّ اسْتَوَىٰ إِلَى السَّمَاءِ فَسَوَّاهُنَّ سَبْعَ سَمَاوَاتٍ ۚ وَهُوَ بِكُلِّ شَيْءٍ عَلِيمٌ
It is He who created for you all of that which is on the earth. Then He directed Himself to the heaven, [His being above all creation], and made them seven heavens, and He is Knowing of all things.
— Surat Al-Baqarah 2:29
The word samawāt (Arabic: سماوات) used in the verse above and elsewhere in the Qur'an is the plural of the word samā' (Arabic: سماء). When used in the Qur'an, it again may refer to the actual skies or to the space in between them and extending all the way to Earth. Linguistically, the plural form should only be used when referring to more than two of a kind, unless used as a literary device. So, do not use them interchangeably.
The phrase al-samā' ad-dunya (Arabic: السماء الدنيا) refers the sky nearest to Earth. On the other hand, the word samā' (Arabic: سماء) is any of the seven skies.
Note that the word samā' (Arabic: سماء), and any of the associated words or phrases you are inquiring about, may be translated as heaven(s) or firmament(s)