I would like to know if possible, however I do not want to know how it would happen but what it would create and how stable that co-existence would be. I would like to know not how it would happen as I known but what the relation between the species. This is no longer a duplicate.
I believe that this question, as asked, is too broad to answer. But I can give you a partial answer.
- Sentient species do not simply appear on the scene. They evolve from non-sentient species.
- On the way to sentience, they usually become the apex predator on their world. A tiger is nothing against a human with a brain.
- If another predator is a near-peer competitor, this pre-sentient species will somehow deal with it.
Of course it remains unclear just how the meeting of homo sapiens and homo neanderthalensis really played out. The early image was "nature tooth and claw" but that might have been wrong.
Sentience is a kinda sticky topic, as there are a lot of skeptics, but there's a lot of evidence that a great many animals on Earth are already somewhat sentient. Humans do seem to be near the top as far as cognitive ability, but many animals have been observed performing ritual activities, using tools, recognizing themselves in mirrors, and even dreaming.
Among those we've identified as the most intelligent, there are only a small handful of highly intelligent species per ecological niche. Corvids, dolphins, octopi, elephants, and apes all occupy vastly different places in their respective ecosystems. It seems a reasonable conclusion would be to only have 1 or 2 intelligent species per ecological role, as they would likely see the others as competition and push them out.
An interesting note, as far as reactions to other sentient species go, most highly intelligent animals with evolved limbic systems (mammals mostly), tend to recognize each other's intelligence and attempt to protect them from time to time. There have been numerous stories about wild elephants protecting humans and dolphins protecting overboard humans from sharks. The nature of the interaction between intelligent species is likely to be highly varied and will depend on the specifics of the type of intelligence those creatures evolve.
How different they could be would depend on the environment they evolved in.
Here's what you would need to achieve this.
Isolated populations that still have plenty of room to evolve. Take a good look at animals in Australia and the Galapagos Islands. There are animals there which you can't find anywhere else, but the humans, they travelled there about 50,000 years ago, likely by sea from Asia. So, what you want are lots of places that are even more isolated than that--bigger oceans that are more difficult to cross, or hazards lasting 10s of thousands of years which divide land, giving each area an opportunity to evolve intelligent life-forms.
When they do meet, they have to cooperate rather than destroy each other, and they have to be genetically distant enough not to interbreed. Neandertals ended up "disappearing" into modern humans. They were different enough to be genetically distinct, but not so different that they couldn't be absorbed into the population. And yes, many think that they were a different species of the same Genus, Homo, which had a common ancestor.
Cooperation will be more likely if they aren't competing for the same resources and if they each have something the other needs. What that could be is up to you.
How different they would be...well...it's your world and that's WIDE open.