If you've been following communities that allow open discussion of BTC and BCH for any decent amount of time, such as /r/BTC, you've undoubtedly witnessed comments such as:
Bitcoin Cash most closely resembles the Satoshi whitepaper, therefore it is the real Bitcoin. BTC stopped being Bitcoin with the introduction Segwit, it no longer follows a chain of digital signatures.
The chain widely traded as "BTC" across all exchanges is the real Bitcoin, as it has been since the market was born.
Bitcoin Cash shares the same genesis block as BTC, and same ledger up until August 1st, 2017. It is Bitcoin.
The longest (most cumulative proof of work) valid chain is Bitcoin.
And of course countless comments akin to:
Bcash is a Roger Ver and Jihan Wu scamcoin designed to trick newbies into thinking they are buying Bitcoin!
With the exception of that last one, these are all valid arguments. So what the hell is "Bitcoin" then anyway? Is it BTC? Is it BCH? Is it neither? Is it both? Let's work our way up.

The Longest Valid Chain is Bitcoin

This one is hard to argue with, so far this "law of Bitcoin" has held true. The longest (most cumulative PoW) chain has remained the one with the most economic activity, and is the one that is traded as "BTC/Bitcoin" to this day. But what constitutes validity? This is not some objectively measurable attribute, rather it varies depending on who you ask.
BCH proponents may argue that the BTC chain is no longer valid, as the addition of Segregated Witness fundamentally changes what Bitcoin is as defined by the Satoshi whitepaper. To these people, BCH is the longest valid chain, and by this definition it is Bitcoin.
Others may argue that the modification of the difficulty adjustment algorithm on BCH, and the addition of replay protection invalidates the chain as "Bitcoin".
Some may not care about any of these details, and recognize both chains as valid, but deem BTC "Bitcoin" as it is the longest chain. Some may even see both BCH and BTC as invalid, and their vision of Bitcoin may exist in the form of Bitcoin Gold, Bitcoin Diamond, or Bitcoin [Insert your Pokemon version here]. A select few may not even feel that any existing implementation of the protocol fits their definition of Bitcoin.

Bitcoin Cash Shares the Genesis Block

Unlike the topic of validity, this is an objective fact. Those who owned BTC at the time of the fork on August 1st, 2017, then owned the same amount on the BCH chain. All history before that point is included in both blockchains. Some may argue this alone gives the Bitcoin Cash chain the right to use the name "Bitcoin", and by the same token, any other coin forked accordingly given the same right. This makes sense, but of course this does not mean the Bitcoin Cash, Bitcoin Gold, etc., are BTC, yet they are still Bitcoin. Think about it like comparing a rectangle to a square. A square is always a rectangle, but a rectangle is not always a square.

The Market Trades "BTC" as Bitcoin

In the beginning there was only one. For the first stage of Bitcoin's life, there was not even a market for it. Intrigued computer geeks and cypherpunks mined their first Bitcoins with their Phenom IIs, Core 2 Duos, or their server CPUs (if they were really dedicated). Next to no one could have imagined they could be holding millions of dollars of value in less than ten years, just for a few days or weeks cracking at some silly algorithm with their PCs. Quickly an over-the-counter market developed, and people sent thousands of Bitcoin to others in exchange for trivial amounts of physical goods or dollars.Soon after, the first real-time exchanges sprung up and offered order-books to exchange Bitcoin against fiat currency. Fast forwarding to today, even as hundreds of new exchanges have come and gone, and thousands more altcoins of all varieties, those very first adopters who mined or bought those coins what seems like many years ago, can still have those coins accepted by virtually any cryptocurrency exchange.
No matter how much BTC has changed, for better or worse, it still holds the top spot among the pack. What isn't certain is if the blockchain currently traded as "BTC" will forever remain the highest valued "Bitcoin" by the market. Many of us hold the belief that a truly free market is the key ingredient to a prosperous and liberating society, and you'd be hard pressed to find a market that is as free as cryptocurrency. We accept that at any given time, the market is right, but we also know that trends can and will change. In the eyes of the market as a whole, BTC is still very much The Bitcoin. For now...

Conclusion

Defining what "Bitcoin" is is no easy task, and it really comes down to the beliefs and values of the individual. Personally, my strongest belief is that a truly free market will always uncover and reward the strongest solutions in the end, and the path to getting there is the most exciting part.
One lesson to take away: The next time you see somebody proclaim what they believe is Bitcoin, don't automatically attribute this to malicious deception if you don't personally agree. Maybe they are shilling for Blockstream Bucks, but more than likely they just feel strongly about what Bitcoin means to them, and that is understandable, especially when so much money is on the line.The best you can do is engage in polite discourse to explain your point of view, in hopes of swaying the market, if only ever so slightly, in the direction you believe in.
So, how do you define "Bitcoin"? Leave a comment and let me know!
As for me, I define Bitcoin as simply: A battle of ideas
- Coinelius (commonly known on reddit as /u/lechango)
 

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  earned 50.0¢
For me is technological BCH real Bitcoin. For the speculators is BTC real Bitcoin. I define Bitcoin as p2p currency and IMHO BCH is one, BTC is no longer one and it will not be anymore.
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   3mo ago
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  earned 0.0¢
Yours is the answer.
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   3mo ago
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Bitcoin = a peer-to-peer electronic cash system. Only 1 chain comes to mind that still has these characteristics, so let's just focus on that one. The market will adjust in its favour eventually, when more people realise BTC is pretty much a useless coin.
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   3mo ago
  earned 0.0¢
Very good explanation, I congratulate you! For me both BTC - BCH are valid, only one will be imposed in the long term, which I believe will be BCH
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   3mo ago
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actually its really simple:

coca-cola (the recipe) is not the same as
coca-cola (the company) is not the same as
coca-cola (the product) is not the same as
coca-cola-light (the product), which is still coca-cola even if you dont like it!

bitcoin (the invention / scheme) is not the same as
bitcoin (the organization / miners+hodlers) is not the same as
bitcoin (the product / transactional network) is not the same as
bitcoin (the token) is not the same as
bitcoin-core (the token), which is still bitcoin even if you dont like it!

It all follows from understanding that the bitcoin whitepaper is not only a blueprint for the product, but also (more importantly) a blueprint for the organization. (further insights in my bitcoin101 article)
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   3mo ago