There is a problem in that I can only describe words to you in terms of other words which are likely to also be mysterious. I'll give you an analogy:
Imagine I have no knowledge of fire and I come to you and ask, "What is this fire that people keep speaking about?" How do you answer me?
You are basically stuck with playing word association games until, after a lot of to-ing and fro-ing you feel confident that I'll recognize fire when I see it and have a fair idea about how it is likely to behave but until I do I won't actually know what the word "fire" actually means.
When I do, I'll realize that I never really knew what it was even though I recognize it. What's more, I need many experiences of fire to really get it and why nobody want's fire that can be fitted nasally. It's a long process - you wouldn't expect me to get fire from a few paragraphs in an internet forum. But I'll eventually gain a solid understanding through theory and experience and then someone else asks me what fire is and I'm stuck playing the same word games you had to use for me.
If you are being honest with us and not just playing at philosophy 101, you are in the position of the person who does not know what fire/photon is and the rest of us are stuck with playing word games.
It's a little bit easier though since you just want to know what these textbooks are talking about - but you won't give us a specific instance from a textbook but instead supply these somewhat vague statements to puzzle over. I've seen stuff kinda like that in textbooks - but not actually like that... I'm left trying to guess where you are coming from which is why I asked for a specific example where you were getting confused: copy one out. But maybe there is enough to work with after all?
Physics textbooks are typically written from a world-view of empirical realism; namely that there is an objective reality "out there" independent of our senses, our sense data tells us useful things about it, and that the truth of any proposition made about this reality cannot be known a-priori. I hope you are familiar with things like empiricism and scientific method. If not: look them up.
Photons are usually written of as objects that have a real existence as "quanta" within the standard model for electromagnetism. In this model, many things come in packages or lumps - it is a
particle model. These packages follow the
Rules of Quantum Mechanics ... which is why they need a special name. Quanta are usually thought of as the smallest bit of something that you can get. eg. a quanta of charge would be the size of the charge on an electron (you can get smaller charges but not by themselves).
A photon is a quanta of electromagnetism - how it manifests depends on how it is detected. In this model "light" and "electromagnetism" are synonyms - but we like to avoid the word "light" due to excess baggage.
So a photon is kinda a small bit of light ... however, a whole lot of photons interacting at a surface would be called "illumination" rather than "light" and a bunch of photons going in a stream roughly the same way would be called a "flux" rather than a "beam of light". You can think of a photon as a bit of light the same way you can think of a grain as being a bit of sand if you like - in that description it would be the smallest bit of light you can get of a particular color - it's not the whole story: remember the fire?
You gave four examples.
The first one is kinda close - except the photon is not an "extended object". Photons arrive in one lump.
The second is close - except it leaves out the wave-like properties.
Which of these you experience depends on how you look - if you are careful though, you get to see some weird stuff which shows it's nature as neither of these things. It is itself.
The last two don't make much sense ... the photon given off in, say, an atomic de-excitation is a lump of light just the same. But it looks like you are struggling with "wave particle duality". Photons are neither classical waves nor particles ... the textbooks are just being inclusive while they break the news to you gently.
Until you have more experience with photons and photon models of nature, for you, a photon will be a step in a calculation that you do to make predictions in physics experiments. You'll just have to settle for understanding them in the abstract like the guy who doesn't know what fire is.
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Caveat: all the above is intended in the context of what is solidly within established science using a simplified language. This science is constantly being tested so at any time there will be some evidence of some kind of exception to some of the things I have stated as fact above. That's just the nature of the beast - you get used to it. In the end we are all just making models. The models are just models -
reality is reality, and the Universe knows far more physics than we do.
For more detail on the "fire" analogy, see Mahasamatman's
"names are not important" speech in Roger Zelazney's
Lord of Light.
