Batuk Bhairo puja idol
Place a Batuk Bhairav Yantra on it. Light a ghee lamp and then worship the Lord with flowers and vermillion. Pray to the lord for achievement and satisfaction. Then combine your palms and chant while meditating on the Lord’s divine form.
The best and auspicious time to worship Kaal Bhairav is the Rahu kaal period on Sundays between 4:30 PM to 6:00PM. Offering such as coconut, sindoor, flowers, mustard oil, black sesame etc. should be offered to Lord Bhairava. Every Shakti Peeth is guarded by Lord Kaal Bhairav and they are known as Bhatuk Bhairav.
According to the story, Brahma grew arrogant and took pride in being the creator of the Universe. Hence Kaal Bhairav severed one of Brahma’s five heads with his Trishul (trident) to punish him. And this was done to remind Brahma that pride, ego and arrogance lead to one’s downfall.
Kaal Bhairav is believed to be the fiercest form of Lord Shiva, both in terms of appearance and nature. He is also referred to as Dandadhipati and Dandapani.
He is known as Shiva, Rudra, Neelakanta, Pashupati, Jagadampati, Maheshwara, Kaal Bhairav, Mahakaal, Mrityunjaya, Kailashnath, Tripuraantaka etc., Even a lifetime isn’t enough to describe Him, this is what Maharishi Vyasa had stated. Hence the answer to your question is that both are merely names of Mahadev.