The only candidates I can confirm for sure didn't boycott were the National Union for Progress candidate (the only Tutsi on the ballot) and the National Liberation Forces candidate.
On 17 July, Minani, Ndayizeye, and Ntibantunganya all withdrew their candidacies after the failure of the talks with the president. Rwasa, while having denounced the election as a fraud, didn't actually withdraw his candidacy, arguing it would be a “waste of time”. The other candidates are fake opponents who only ran to give some legitimacy to the election.
Jacques Bigirimana, who didn't boycott, appeared on the ballot as the FLN candidate.
Agathon Rwasa, who may have boycotted and has called the elections a sham, was listed as an independent.
Most international media has called Bigirimana's faction the break away faction.
So I'm guessing there was a split over whether or not to back the government, with Rwasa taking the actual supporters but Bigirimana keeping the name thanks to being friendly with the government.
In order to weaken the opposition, Nkurunziza and his interior minister have used the so-called “Nyakurisation” strategy: internal divisions within opposition parties are created and supported by the regime (notably by the infiltration of supporters of the president in the parties) ultimately leading to a split between an anti- and a pro-government factions with the latter being recognized as the sole legal owners of the party appellation.
The “Nyakurisation” term has been coined after the 2008 government-sponsored split within the Front for Democracy in Burundi (Frodebu), historically the main Hutu party. The pro-government faction led by Jean Minani then launched the “genuine Frodebu” (Frodebu-Nyakuri) and joined the government of Nkurunziza. Minani however broke later with the Burundian president over the latter's decision to run for a third presidential term.
Meanwhile, the anti-government faction, called the Sahwanya-Frodebu, has remained in opposition to Nkurunziza and decided not to field a candidate in this year's election. As a consequence, Ntinbantunganya, one of the historical leaders of the party, was expelled in early 2015 for still running for president as an independent candidate. Few months before that, Ndayizeye was also expelled from the Sahwanya-Frodebu after his unsuccessful attempt to reunite the two factions of the Frodebu which by now both stand in opposition to Nkurunziza.
Nyakurisation was also used to deprive Rwasa of the leadership of his National Liberation Forces (FNL), his guerrilla-turned-political party. After months of internal struggles in the FNL, Rwasa was expelled from the party in August 2013 and replaced as leader by Jacques Bigirimana, a partisan of an alliance with Nkurunziza, who ran this year as a token candidate. Earlier this year, Rwasa was also prohibited by the Interior Ministry to use the FNL symbols in his electoral campaign.
The latest political party broken by the Nyakurisation is the National Union for Progress (Uprona), the former Tutsi supremacist party which ruled the country from the independence to the 1990s. The Uprona had been part of the government until February 2014 when it decided to enter into opposition to protest against Nkurunziza's decision to run for a third term. Shortly thereafter, the legitimate leader of the party, Charles Nditije, seen his leadership being disputed by a concurrent, more favorable to the president.
After a legal battle, the pro-Nkurunziza concurrent of Nditije was recognized as the legitimate leader of the Uprona while the Nditije's faction (the largest one) lost the right to call itself the Uprona. The “legal” Uprona fielded a nobody as token candidate in this year's election while, in a bizarre twist of events, Nditije ended up supporting the candidacy of Rwasa, despite the latter's past as a Hutu extremist guerrilla leader. Ironically, in the mid-2000s, Nkurunziza's own Hutu guerrilla actively helped the Tutsi-dominated army in the military campaign the latter waged to eradicate Rwasa's FNL.
Beside personal rivalries, there is also a religious cleavage between Rwasa and Nkurunziza. The former, generally described as a religious fanatic nutcase, is a practicing Catholic who maintains close links with the Catholic Church (which has opposed Nkurunziza's third term). Meanwhile, Nkurunziza, also a religious fanatic nutcase, is an evangelical born-again.