It basically means you read the paper and write the code to do what the paper describes yourself.

If you start with their code base, then your work is derivative of that copyrighted work and the question becomes a bit more complicated.

Yes, the line is fuzzy. However, it's typically very easy to stay on the "not copyright or license infringing" side of the line if you make an honest effort to rewrite the code from scratch and simply use their code base to check your understanding of the algorithm.

Again, IANAL but changing a for loop to a while loop is probably not sufficient to distinguish between their work and yours. Rewriting the code in another language may be. Rewriting it in the same language but making substantial changes to (for example) user interface, data preprocessing, training data, hyperparameters, etc... may be.

Edit: courts and lawyers usually aren't too concerned with technical details. Think of it like a book. The same story gets told over and over again by different authors who use different words to tell it. Your implementation needs to tell the same story but in different words, basically.