Sine vs Sine: understanding the differences

Question

I was using the textbook A History in Mathematics by Victor J. Katz. I saw a theorem from Nasir al-Din al-Tusi. The way the theorem is written in the book is like this:

In any plane triangle, the ratio of the sides is equal to the ratio of the sines of the angles opposite to those sides. That is, in triangle ABC, we have AB:AC=sin(angle ACB):sin (angle ABC). [Note that since we are considering a ratio it is irrelevant whether we use Sines or sines.)

This theorem is about the law of sines. My question is about the last sentence in parenthesis.

What is the difference between Sine and sine?

Answer 1

Six pages earlier, at the beginning of 9.6.1, the first subsection on Islamic trigonometry, a parenthetical remark notes:

The Islamic sine of an arc, like that of the Hindus, was the length of a particular line in a circle of given radius $R$. We will keep to our notation of "Sine" to designate the Islamic sine function

Additionally, in 8.7.1 on Indian trigonometry, the book explains:

In what follows, we generally use the word "Sine" (with a capital S) to represent the length of the Indian half-chord, given that the half-chord is a line in a circle of radius $R$, where $R$ will always be stated. We reserve the word "sine" (with a small s) for the modern function (or, equivalently, when the radius of the circle is 1). Thus, $\mathrm{Sin}\,\theta=R\sin\theta$.

I have not seen this convention outside of this book. As noted in the comments, in modern mathematics, some might use a capital letter to denote a restriction of the domain of the sine function.