The difference between "Kudos" and "Props"

I've looked through the definitions of kudos and props:

According to Cambridge Dictionary, the definition of kudos is the public admiration that a person receives as a result of a particular achievement or position in society, whilst props means respect for someone.

So, "kudos" connotes approval and admiration, and "props" implies respect.

However, I'm wondering if there are any cases in which one of them are fine to employ while the other would be inappropriate or wrong to use in the same sentence.

The main difference is in how formal it comes across.

"Kudos" is considered a 'real' word while "props" is considered slang but neither are very formal.https://www.etymonline.com/word/kudos

"Kudos", usually used as an interjection like 'congratulations', comes from UK university slang, which means by now it is fairly formal. For example:

Kudos! Your excellent presentation to the CEO will really have you climbing the org chart!

"Props", short for 'proper respects', comes from US hip hop slang, so it is more easily recognized there than in the UK.

Gotta give props to that kid for that stunt. When does he get out of the hospital?

As someone on reddit said:

"Props is for friends, kudos is for work."

Here are some cases which fulfill your criteria of providing examples in which one word would be appropriate and the other would not. The degree of inappropriateness is not absolute but I still think these are good examples.

In the following paragraph I am using both the word "kudos" and "props." I believe that interchanging the two words change the meaning of the paragraph. Thus, both the sentence that contains "kudos" and the sentence that contains "props" are examples of sentences in which it is correct to use one but not the other.

"Jim knows how to present his work in a way that makes it seem to be great. He wins the productivity awards every time. But, we all know that his work is insubstantial and shaky. Someone else generally has to redo what he has done when we notice that it's starting to fall apart. Bob, on the other hand, is the best worker in our firm. He not only does all of his work flawlessly, he picks up the slack for everyone else, especially for Jim. I guess that's life. Jim gets the kudos from the higher-ups. Bob must be content with our sincere props."

In the above paragraph, interchanging props and kudos would give an inappropriate meaning. It sill would be grammatically correct, of course. But I think that meaning is the issue here.

But, can I do it without using multiple sentences to set it up? How about the following?

"Jim is a sociopathic sycophant who has figured out how to get all the kudos and bonuses from our out-of touch management while Jim, the most diligent and effective worker in the group, must be content with the sincere props of his closest colleagues."

In the first phrase of that sentence, the fact that I said "out-of-touch" management makes it hard to believe that management could actually have respect for Jim. The statement implies that they are responding to superficial things. So "props" would be a bad fit. In the last portion, the word "sincere" is a more appropriate adjective for "props" (sincere respect) than for "kudos", though you could have sincere public admiration or sincere praise. But by mentioning the "closest colleagues" I am implying that this is not public. The word "props" in that sentence implies a more personal feeling as opposed to public admiration. So, interchanging either word in that sentence would significantly alter the meaning.