Is a black hole made from a anti-matter star the same as a ordinary black hole? Would a black hole from a star made of anti-matter be the same as a blackhole made of ordinary matter?.
To put a formal answer to this question, a black hole made of anti-matter would be indistinguishable from a matter black hole. Black holes are dubious objects, but it seems likely that it makes no sense to talk about an "anti-matter black hole" as once the matter goes into the black hole, be it matter or anti-matter, it ceases to have properties that define it as matter or anti-matter. The No-Hair Theorem for black holes states that, among a few other properties, a black hole is defined only by it's mass and net charge. The matter state of individual particles which fell into the black hole play no part in that description.

In fact, there is a vigorous debate as to whether or not "information" is conserved for black holes. E.g., if an anti-matter particle fell into a black hole, could you, at a later time, pull out a particle of the same properties or would you get out something of completely randomly new properties, not tied to the original matter. This in part plays into your question because it indicates that there is still a lot of uncertainty regarding the loss of information (including if the particle is anti-matter or matter) as particles fall into a black hole and whether not feeding anti-matter into a black hole actually makes it an anti-matter black hole or just simply a black hole.