I recently arranged my Mom's funeral services at a Wesleyan service after she died of cancer this past Dec. 8, so I hope people don't mind if I offer what I found about the subject from a Wesleyan website:
WHO ARE THE WESLEYANS
The Wesleyan Church is an evangelical, Protestant denomination. We offer the good news that faith in Jesus Christ makes possible a wonderful personal relationship with God, a holy life empowered by His Spirit for witness and service, and assurance of eternal life in heaven. Our ministries emphasize practical Bible teaching, uplifting worship, and special programs to meet a variety of life needs.
With World Headquarters in Fishers, Indiana, The Wesleyan Church has nearly 400,000 constituents in 5,000 churches and missions in 80 countries of the world. Formed in 1968 resulting from the mergers between several like-minded groups, dating back as far as 1843, The Wesleyan Church has its roots in John Wesley’s Methodism.
Wesleyan Source
I think that DeaconDean is right that it must be some kind of hybrid between the two religions since Wesleyan is Methodist and not Baptist.
Maybe the member on the other website invented it to describe their own personal beliefs. Maybe they are a former Wesleyan turned Baptist, but they retain some of their Wesleyan beliefs.