RE: Bitcoin Unlimited Is Gaining On SegWit, Could It Overtake? Could We Do Both Even? (The Cryptoverse #191)
They are the same coin, using the same blockchain, but a different client wallet. Bitcoin Unlimited has a differing vision of future development than the Bitcoin Core developers. They signal that difference by using a different name for the wallet they develop. That is a simplified answer.
Bitcoin Unlimited was created to push for development of 'larger block sizes', which the Bitcoin Core developers were opposed to implementing.
You might look into the terms 'hard fork' to understand how blockchains change the way they function. It requires a consensus between the developers and miners and the greater community of Bitcoin users for a hard fork to be successful. There is some controversy atm, because the number of transactions being processed is increasing and causing delays and increased transaction fees.
The two different camps of thought are offering two different solutions to those issues.
Wow. Thank you for this! Thank you so much!