Key generation is just a process
Anything is "just a process", executing any algorithm is "just a process". So lets ignore this part of the sentence as it doesn't make sense.
while key scheduling is about the calculation of key in the algorithm.
That's right. If the algorithm requires a key in a different form, e.g. expanded from the original form, then the key schedule is the part of the algorithm that performs that calculation.
However, this argument is true when we're talking in the context of a block cipher. Key schedule could mean other things in other contexts.
So now the sentence reads "Means (the process or procedure that is taking place in generating a key) is called key generation, am I right here?".
That sentence is self-evident. However, as long as "generation" is not further clarified, it carries no weight.
Moreover, what we will be called if we calculate a key using any method in our algorithm
That depends if we're still talking in the context of a block cipher I suppose. If you're deterministically transforming your key within your algorithm then I suppose you can call it a key schedule. You can also call it something else; it is your algorithm after all.
Just for example say that I calculate a key using different chaotic equations. Combine these equations in a particular way and generate a final key.
If you do that deterministically and within your algorithm then nobody would raise an eyebrow if you call it a key schedule. It would help if your algorithm would be a block cipher.
They would raise an eyebrow if you try and use it to increase the key strength or if the method takes lots of time, because that is not what key schedules are generally about.
Is it will be key scheduling or key generation?
Key generation supposes randomness, and randomness supposes some source of entropy. If no source of randomness is given then we can confidentially say that it is not key generation.
If it is a key schedule is already discussed above. There are other options such as key establishment. However, if there is a single key as input, and if the supposed key schedule is happening within your algorithm, then it makes sense to call it a key schedule.