Were they just locals who converted by the Ottomans? Or did they move into the area from other parts of the Ottoman Empire?
Also, and this is a slightly different question, were Bosniaks (and Albanians?) a different ethnic group to others in the area before converting to Islam, or was their ethnicity defined by being Muslim (ie being a Muslim in that area made you a Bosniak)?
Bosnians/Bosniaks is a disputable term by many scholars due to its recency and dubious, equivocal historical 'evidence' that pro-Bosnians use to back it up. The terms "Bosnians/Bosniaks" were used to imply geographic provenance, and not an ethnic group. The people that we now know as Bosnians/Bosniaks were simply called 'Muslims' before the Yugoslav wars.
On the other hand, Albanians have always been a separate ethnic group, which is proven by numerous unequivocal writings in possession of the Vatican, as well as scriptures by travelers throughout several centuries. The earliest documents using the name Albanians/Arvanites have been known to date the fifth century. Albanians claim that they are descendants of the Illyrians, which would make them one of the longest residents on the Balkans, but this claim is disputed by nationalist academics from surrounding countries. To further prove the Albanians' uniqueness and authenticity - the Albanian language is a sub-branch for itself in the European tree of languages. There is no other language similar to it.
To answer your question regarding Albanians: The truth is that the Albanians were never deeply connected to religion - they were more closely attached to their tribe/region. As such, a lot of tribes/regions were constantly in violent conflict with each other which meant that the men had to be armed at all times. This is considered to be (most likely) the biggest reason why the majority of Albanians converted to Islam. Muslims in the Ottoman Empire, among other benefits, were allowed to carry a gun with no problems. Of course, it didn't happen overnight, there were resistances.
However, Albanians still have a significant percentage of Orthodox and Catholic Christians. This fact is often ignored. Albania is one of the rare cases in the world where all three religions coexist without problems.
PS: If you intend to read on Albanians from academic from surrounding countries, take everything with a dose of skepticism. Albanians are literally alone against all in the region, meaning the nation is constantly targeted by negative propaganda from its neighbors on a daily basis.
Not a mod, but you should probably check the FAQ and specifically this thread out. /u/UrbisPreturbis provided a rather substantial answer to the question, in my opinion.