Which is wider, 내 or 시내?

Answer: A 내 is wider than a 시내.

내 is the pure Korean word for stream, which is wider than a 시내, the pure Korean word for brook or small stream. The 시 in 시내 is most likely a reduction of the pure Korean word 실, which means thread, yarn, or string. That would mean 시내 would literally translate as thread-like stream.

The Sino-Korean word for stream or brook is 계천 (溪川), which is a combination of the characters 溪 (계), which means brook (시내), and 川 (천), which means stream (내). In downtown Seoul, for example, there is a stream named Cheonggyecheon (청계천 淸溪川 ), which literally means clear (淸) stream (溪川).

The characters 溪 (계) and 川 (천) are not normally used by themselves but rather as part of other words, such as in the names of streams, or in such words as 개천 (開川), which literally means open (開) stream (川) but generally refers to man-made ditches or open sewers. The pure Korean word for ditch or open sewer is 도랑. Also, a very narrow ditch or stream is called 실개천 (실開川), which literally means thread-like (실) ditch (開川). By the way, notice that 계천 (溪川) and 개천 (開川) sound similar, so just remember that the first one means stream and the second one is more of a ditch.

Finally, 개울 is another pure Korean word that can translate as either brook (시내) or ditch (도랑). You would have to consider the context of the sentence or writing to decide which translation to use. 실개울 means small stream or ditch. Again, 실 is the pure Korean word for thread, yarn, or string.