Lingayats and Veerashaivites are often considered the same Shaivite sect. However, there are many who consider them distinct to each other. What is the difference between the two?
Well just stating the differences between the two as has been stated here in the following article:
Who are Veerashaivas
Veerashaivas are worshippers of Lord Shiva. They precede Basavanna, the founder of Lingayatism. Veerashaivas do not worship any God other than Shiva and can be found spread across India. Pashupatha Shaiva, Soma Shaiva, Dakshina Shaiva, Kala Mukha Shaiva, Lakula Shaiva, Yavala Shaiva, Samanya Shaiva, Mishra Shaiva, Shuddha Shaiva, Adi Shaiva, Anu Shaiva, Avantara Shaiva are some of the sects within Shaivism. Veerashaiva is one such sect and people from the community are found largely in Karnataka, Andhra Pradesh and Kerala. Those who consume non-vegetarian food call themselves Kshatriya Shaiva while those who are vegetarians call themselves Brahmana Shaiva. All sects of the Veerashaiva follow the 'Pancha Peeta', five mutts. Kashi mutt, Rameshwaram Mutt, Ujjaini Mutt, Rambhapura Mutt and Srishaila Mutt are the core holy places for the community.
Who are Lingayats?
Lingayats are followers of Basavanna and his teachings. Veerashaivas in Karnataka, influenced by the preachings of Basavanna adapted the same into their lives and faith. Basavanna's teachings were incorporated to base sects that led to the formation of new sects like Banajiga Lingayat, Panchamasali Lingayat, Ganiga Lingayat, Gowda Lingayat and Veerashaiva Lingayat.
There are many differences
Veerashaiva and Lingayat ways of life are different. Their beliefs, practices and faith are different. Veerashaiva worship Lord Shiva, the one mentioned in Hindu mythology. But the Shiva that Basavanna referred to is not the Hindu mythological Shiva. Basavanna's Shiva is a formless, seamless figurative entity. Lingayats argue that this was the very reason that Basavanna never mentioned about the Hindu mythological Shiva in any of his Vachanas. In terms of religious practice, Basavanna propagated only the worship of Ishta Linga. He did not encourage rituals and ceremonies of offering, prayer and sacrifice. Veerashaivas, however, encourage such rituals in stark contrast. Basavanna had suggested wearing of the Ishtalinga on one's neck but Veerashaivas have done away with the practice.
Hopefully it may help you in some way.