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Are there sharp distinctions between primordial black holes and the usual black hole?
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Can a primordial black hole smoothly become massive to be a black hole?
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Can a black hole smoothly become less massive to be a primordial black hole? Say by evaporation?
Some facts:
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Primordial black holes masses can be far below stellar mass, thus far less than black hole masses.
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Primordial black holes are a hypothetical type of black hole that formed soon after the Big Bang. In the early universe, high densities and heterogeneous conditions could have led sufficiently dense regions to undergo gravitational collapse, forming black holes. Yakov Borisovich Zel'dovich and Igor Dmitriyevich Novikov in 1966 first proposed the existence of such black holes. The theory behind their origins was first studied in depth by Stephen Hawking in 1971. Since primordial black holes did not form from stellar gravitational collapse, their masses can be far below stellar mass (c. 4×$10^{30}$ kg).
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Primordial black holes could be a type of dark matter called MACHOs, which stands for massive compact halo objects, because astronomers think they're found in the halos, or outskirts, of galaxies. Such black holes would be difficult to see if they're simply floating quietly in space and keeping to themselves.
Best Answer
The only properties a black hole has are its mass and spin (and, theoretically, electric charge, but we don't expect to find electrically charged black holes in Nature).
The only difference between a primordial black hole, and a black hole of stellar origin, is when the black holes are made. Primordial black holes (if they exist) are formed by processes in the early Universe such as during a phase transition. Stellar origin black holes form from stellar collapse. Therefore, a primordial black hole can't become a stellar origin black hole, and vice versa.
However, if you had two black holes, there would be no way to do experiments on the black hole to say which was primordial and which was stellar origin. The way we would distinguish them is based on theory of stellar evolution, which puts a lower bound on the mass of black holes, while primordial black holes can be of lower mass.