Bhagat and Bhakt are different spellings of the same word. and same with Bhagati and Bhakti. The difference in spelling emerges out of different pronunciations and changes to a word over time, and also when it enters into other languages. It's spelled Bhagat and Bhagati in Sri Guru Granth Sahib Ji. My name comes from Sri Guru Granth Sahib Ji hence it's Bhagat, but I had a friend pronounce it as Bhakt. Both are fine. Bhagat/Bhakt is one who practices Bhakti/Bhagati (Yog) in one form or another.
You'll find Kanwal and Kamal are the same, meaning lotus. Vishnu and Bishan, the Almighty. Purakh and Purush, meaning Man as in Karta Purakh, Creator Man. Sikh and Shishya meaning disciple of a Guru. Gobind and Govind, referring to Krishna. That leads to Krishan, Krishna, Kisan, Kishan. And so on.
And I think one of the member's names here, Ambarsaria, is the same as Amritsaria meaning one from Amritsar. Then there is Harimandir and Harmandar, the Golden Temple.