Halal mean lawful in Arabic, and used to describe objects rather than an action. Normally when describing an action that is allowed we would say it is obligatory (fard/wajib), recommended (mandoub) or permissible (mubah).
Haram means prohibited or unlawful, this term is both used for objects as well as actions. When describing an action that is not allowed we would say it is prohibited (haram) or disliked (makrouh)
Dhabh (ذبح) The meaning of the word ‘dhabh’ can be found in Bukhari
This method is used for birds, cattle, sheep and goats, whereby the animal is laid down on its right side and the blood carrying veins are cut.
Nahr (نحر) This method of is used for slaughtering camels and is done by cutting the carotid arteries at the root of the camels neck. The camel’s front legs are bent at the knee and thereafter tied.
THE ISLAMIC PRACTICE IS TO SLAUGHTER THE ANIMAL
The practice of slaughtering in Islam has always been to apply a sharp blade to the neck of the animal.
Abu Yaala Shaddad bin Aws (ra) reported that the Messenger (saw) said:
إِنَّ اللَّهَ كَتَبَ الإِحْسَانَ عَلَى كُلِّ شَىْءٍ فَإِذَا قَتَلْتُمْ فَأَحْسِنُوا الْقِتْلَةَ وَإِذَا ذَبَحْتُمْ فَأَحْسِنُوا الذَّبْحَ وَلْيُحِدَّ أَحَدُكُمْ شَفْرَتَهُ فَلْيُرِحْ ذَبِيحَتَهُ
“Verily Allah has prescribed proficiency in all things. Thus, if you kill, kill well; and if you slaughter, slaughter well. Let each one of you sharpen his blade and let him spare suffering to the animal he slaughters.” [Sahih Muslim] #5167
And Allah (swt) says,
فَصَلِّ لِرَبِّكَ وَانْحَرْ
Therefore turn in prayer to your Lord and sacrifice (to Him only) [Surah Al Kawthar 108:2]
In the above verse Allah (swt) has twinned slaughtering with prayer, both are ritual acts. The ritual act in Islam has a set form which must be done in accordance with the example of the Messenger Muhammad (saw), who said
خُذُوا عَنِّى مَنَاسِكَكُمْ
“Take (learn) your ritual acts from me” [Musnad Ahmed] #14793