Essentially, I'm in the pre-planning stage of writing a short story where I want there to be a "normal" species (think human) that interacts with a species that for one reason or another doesn't differentiate themselves from other living things. There could definitely be religious reasons for such a culture to exist, but I'm imagining a scenario where they (the other species) never even had the idea to differentiate themselves from their planet's co-inhabitors (if it has any).
One potential would be a Gaia-like ecosystem. If every creature acts as part of a greater whole then even the parts that develop self-awareness may not develop a concept of difference from the whole.
Even if these creatures become quite advanced their connection to nature (to them their connection to.. well, everything) can remain dominant over their individuality as a species.
Plus points if the ecosystem supports a lot of cross-species (ok, taxonomically inaccurate but it’s an alien biosphere, so hey) breeding, with the sentient species often giving birth to more animal species and vice-versa.
They can hybrid with most life on their planet.
Sure banana-biped hybrids aren't very useful, but if they are viable it might not make a lot of sense to call them a different kind of thing from biped-biped lines.
Different lineages are better at different things, the sentient ones are good at thinking, but they need ox-like ones for heavy lifting or horse-like ones for speed and giving them more intelligence wouldn't really help anything they care about.
This strongly suggests cannibalism and bestiality aren't taboo.
"That fruit comes from my third cousin four times removed. Go ahead and eat him; that's how he will propagate my five times removed cousins. I can't right now because it would interfere with the tapeworm children I'm currently gestating."
Your other species aren't just animals... They are animal plant hybrids. Your species do not eat like humans do, they consume nutrients from the ground in the same way that plants do. Sticking part of themselves into the ground (some sort of probing appendage on the head or feet), for a period of time functions both as a sleep and food combination.
The result of such bizarre anatomy is an interesting philosophy. The other species sees themselves as connected to every other species on their planet. For instance, when an animal dies/defecates/leaves a piece of itself somewhere on the planet eventually the substances that make up the dead animal sinks into the land and function as food for the other species.
Going strongly with the phrase "you are what you eat", the other species has come to the conclusion that since the planet is what sustains them and they are in such constant contact with the planet, they feel as one with it. That oneness extends out to every other being.
To further reinforce this, the other species "mates" via erupting spores into the air. When the spores in the air come into contact with spores from another member of the other species, there is a chance that the spores will bond together and start to form another member of the species.
Since the spores are made from food and food comes from the planet and the planet is filled with other forms of life... Whats the difference between the other species and everything else? NOTHING! The other species proclaims. If a bundle of cells is not the other species now, given enough time, the bundle of cells will eventually become the other species again.
The other species might refer to this as the real cycle of life and refer to humans (if you did want the other species to see humans as different) as "noncycled".
Your last line certainly suggests one possibility. If there were no other species on their planet then there would be no need for a word meaning 'other species'.
Languages vary in how malleable they are when confronted with new evidence but it is plausible that this group would not update their language when they eventually did encounter 'alien' species.
Almost by definition, sentience requires a sense of self, which almost automatically includes a sense that one is if not unique, at least differentiable from other beings. So to not recognize differences between species might be an argument that they aren't sentient.
There's lots of memes about cats and dogs thinking of everything as nothing other than other cats/dogs, albeit larger, smaller, or having the wrong number of legs.
As you said, one could easily imagine a culture that chose to see no differences between themselves and what might be used as pack animals. But eventually they have to eat, and that would require a decision on what's lesser enough that it's okay for it to die so they can live.