The bitcoin cryptocurrency works on a blockchain software that's unique from that of alcoins' blockchain softwares.
blockchain itself is not a "software" it is a database. as the name suggests it is "a chain of blocks" which means blocks of data that each is linked to the previous one like a chain.
considering the fact that a very large percentage of altcoins have copied bitcoin, their blockchains are exactly the same.
What I really desire to know is how does the bitcoin blockchain work differently from altcoin blockchain and what are the core programming technologies behind it?
i'm not sure what you are asking here, but as far as blockchain is concerned i can think of three topics: the block structure, the way the blocks are linked together, and the method used to set a cost for creating the blocks.
1) the block structure is not really that important. it is the way transactions are serialized and put inside a block, what part is there to be hashed for part 3,...
2) the way blocks are linked together is (in bitcoin) with each new block having a reference to the hash of the previous block. there are other methods in different chains that someone more familiar with them should answer here.
3) the "cost" is the proof of work for bitcoin and all the similar coins which needs to be an irreversible one way function that could be adjusted to be fast or slow depending on the needs of the network (difficulty) and it should produce a result that could be compared with a desired target. the function is usually a hash function (double SHA256 in bitcoin, Keccak256 in ethereum, scrypt in litecoin, prime gap in GapCoin,...) and the target is usually an integer (little endian 256-bit number in first 3 and a set prime gap in GapCoin).