The Madhva sampradaya mark two vertical lines representing Krishna's 'lotus feet'. In between a vertical black line is made from the daily coal of the 'yajna-kunda' (fire sacrifice). In this sampradaya, the process of worship involves 'nitya-homa', or daily fire sacrifices to Narayana or Krishna. The remnant coal of the puja (worship) is used each day to mark the forehead. Underneath the black line, a yellow or red dot is added to indicate either Lakshmi or Radharani. Those who did not perform daily fire sacrifice wear the simple two line tilak only.
The mark here is called Sricharanam. Members of the Sri Vaishnava tradition form tilak with two lines representing the feet of Narayana, with a red line in the middle which representing Lakshmidevi. A small line on the top bridge of the nose which represents that the wearer belongs to the Thenkalai subsect. Because the Sri Vaishnava sampradaya begins with Lakshmi, and because they approach Narayana through Lakshmi, their tilak reflects this process of surrender, know as Saranagati (or sometimes also Prapatti). Within Sri Vaishnavism, this process of surrender (sarangati) to Vishnu. A variant to this is found within the Ramanandi sect, begun by Ramananda, who wear a similar tilak design but in reference to Sita and Rama (whom their devotion is focused upon) rather than Lakshmi and Narayana.
In the Gaudiya Vaishnava sampradaya the tilak is usually made out of mud from Vrindavan. The main tilak is basically identical to the Madhva tilak. The slight difference arose due to the emphasis on the chanting (japa and kirtan) in the Gaudiya tradition. In Chaitanya Mahaprabhu's line, chanting is given as the essential devotional (bhakti) activity to be performed in Kali yuga in preference to fire sacrifices. As such, the black line made from the ash of the fire sacrifice is not included. The second difference arose due to Chaitanya Mahaprabhu's process of approaching Krishna. In the Gaudiya line devotees generally approach Radha and Krishna through a servant such as Tulsidevi. To indicate this, the red dot representing Radha is replaced with a tulsi leaf offered at the base of Krishna's feet. In Gaudiya belief only through the mercy of Tulsi (or another pure devotee) can pure devotion to Radha & Krishna or Krishna & Balarama be awakened.
In Nimbarka Sampradaya, the tilak is made of Gopi-Chandana (the clay from Gopi Kunda lake in Dwarka, Gujarat), as described in the Vasudeva Upanishad. It starts at the bridge of the nose and continues as two vertical lines to the top of the forehead. This is said to represent the temple of God. Within these lines, between the eyebrows is a black dot, made from the slate found in Barsana, Uttar Pradesh, the sacred birthplace of Radha. This is said to represent God as Radha and Krishna together. This tilak personifies the tenets of the Sampradaya, that God is Radha and Krishna together, none else. It is supposed to have been first given to Nimbarka at the time of his initiation to the sage, Narada. The tilak is first given to an initiate by their guru at the time of initiation, and after this, daily the devotee will remember his guru before he adorns the tilaka on his head.