from that of the nature of being.

No. They are separate.

The words, distinct from indicate they are not the same.

The science of phenomena is a science on its own. It deals with the mind. Intelligence, intellect, acquired knowledge and reason.

The science of the nature of being is about life, being alive, existing.

Phenomena is the study known as noology. The science related to the nature of being is known as ontology.

Yes, in the sentence, "that" refers to "the science."

Thank you

Yes. This is an example of the figure of speech "ellipsis", where a word or phrase is used twice but only spoken once.

"Relating to the science of phenomena as distinct from the science of the nature of being.

A figure of speech is a departure from normal discourse for the purpose of emphasizng or embellishing what is being said. The basic figure is the simile: "You are like a dog." The figure simply says a comparison. A metaphor sets the two equal: "You are a dog." Then we have a big word, hypocatastasis. That is a Greek word for name calling: "Dog!"

You can learn more about figures of speech from this free book:
https://www.google.com/search?q=figures+of+speech+bullinger