If Isha means evening and leil means night, why the night prayer is called Isha, as Allah request to pray at morning, before sunrise, at evening before sunset and in the darkness of the night ? and neither the word of Asr and Maghrib appears as prayer times. Please note that the Quran is complete and never did Allah permitted to refer to any other book for explanations.
Allah says in the Qu'ran:
يَا أَيُّهَا الَّذِينَ آمَنُوا لِيَسْتَأْذِنْكُمُ الَّذِينَ مَلَكَتْ أَيْمَانُكُمْ وَالَّذِينَ لَمْ يَبْلُغُوا الْحُلُمَ مِنْكُمْ ثَلَاثَ مَرَّاتٍ ۚ مِنْ قَبْلِ صَلَاةِ الْفَجْرِ وَحِينَ تَضَعُونَ ثِيَابَكُمْ مِنَ الظَّهِيرَةِ وَمِنْ بَعْدِ صَلَاةِ الْعِشَاءِ ۚ ثَلَاثُ عَوْرَاتٍ لَكُمْ ۚ لَيْسَ عَلَيْكُمْ وَلَا عَلَيْهِمْ جُنَاحٌ بَعْدَهُنَّ ۚ طَوَّافُونَ عَلَيْكُمْ بَعْضُكُمْ عَلَىٰ بَعْضٍ ۚ كَذَٰلِكَ يُبَيِّنُ اللَّهُ لَكُمُ الْآيَاتِ ۗ وَاللَّهُ عَلِيمٌ حَكِيمٌ
O you who have believed, let those whom your right hands possess and those who have not [yet] reached puberty among you ask permission of you [before entering] at three times: before the dawn prayer and when you put aside your clothing [for rest] at noon and after the night prayer. [These are] three times of privacy for you. There is no blame upon you nor upon them beyond these [periods], for they continually circulate among you - some of you, among others. Thus does Allah make clear to you the verses; and Allah is Knowing and Wise.
In this verse, Isha is known as the night prayer.
In another verse, Isha is known as a period.
وَجَآءُوٓ أَبَاهُمۡ عِشَآءً۬ يَبۡكُونَ
And they came to their father at night, weeping
Therefore, Isha is the evening prayer or period which corresponds to the segment of the night when there is total darkness or at least when as much scattered light that can disappear leaves the night sky.
So an 'Isha' prayer is a night time prayer, different from a 'Maghrib' prayer which is one that is established just after 'sunset' (ghurub). >>Source<<
On the other hand, 'Layl' (night) is a point after sunset (not at sunset - ghurub) which leads to total darkness till the point of dawn (fajr).
Quran 2:187 states:
أُحِلَّ لَكُمْ لَيْلَةَ الصِّيَامِ الرَّفَثُ إِلَىٰ نِسَائِكُمْ هُنَّ لِبَاسٌ لَّكُمْ وَأَنتُمْ لِبَاسٌ لَّهُنَّ عَلِمَ اللَّهُ أَنَّكُمْ كُنتُمْ تَخْتَانُونَ أَنفُسَكُمْ فَتَابَ عَلَيْكُمْ وَعَفَا عَنكُمْ فَالْآنَ بَاشِرُوهُنَّ وَابْتَغُوا مَا كَتَبَ اللَّهُ لَكُمْ وَكُلُوا وَاشْرَبُوا حَتَّىٰ يَتَبَيَّنَ لَكُمُ الْخَيْطُ الْأَبْيَضُ مِنَ الْخَيْطِ الْأَسْوَدِ مِنَ الْفَجْرِ ثُمَّ أَتِمُّوا الصِّيَامَ إِلَى اللَّيْلِ وَلَا تُبَاشِرُوهُنَّ وَأَنتُمْ عَاكِفُونَ فِي الْمَسَاجِدِ تِلْكَ حُدُودُ اللَّهِ فَلَا تَقْرَبُوهَا كَذَٰلِكَ يُبَيِّنُ اللَّهُ آيَاتِهِ لِلنَّاسِ لَعَلَّهُمْ يَتَّقُونَ
Permitted for you (in the) nights (of) fasting (is) the approach to your wives. They (are) garments for you and you (are) garments for them. Knows Allah that you used to deceive yourselves, so He turned towards you and He forgave [on] you. So now have relations with them and seek what has ordained Allah for you. And eat and drink until becomes distinct to you the thread [the] white from the thread [the] black of [the] dawn. Then complete the fast till the night. And (do) not have relations with them while you (are) secluded in the masajid. These (are the) limits (set by) Allah, so (do) not approach them. Thus makes clear Allah His verses for [the] people so that they may (become) righteous.
The night is being referred to as layl(leil).
Quran 2:187 is saying layl until the white thread of dawn appear to you distinct from its black thread.
And Allah knows best.