Imagine that the English language has a similar writing system. (The specifics here are a simplified example that I invented, not Grandma’s original explanation, which was more abstract and general, with many books and essays and dictionaries and photographs of cuneiform tablets waved about.)
Suppose, then, that a stylized picture of a bee represents either the insect "bee", or the sound of the syllable /bee/, or the word that sounds like /bee/ that means "to exist" (to be). And a stylized picture of a deer represents either the animal "deer", or the sound of the syllable /deer/, or the word that sounds like /deer/ that means "precious" (dear). The symbols [deer] [bee] put together also represent the similar-sounding word "Derby", which can be a place in England "Derby", the horse-racing contest held there "the Derby", a style of small round men’s hat that originated there "a Derby" or a particular hat in this style, or a racing contest in general e.g. "roller derby", "demolition derby". Or [deer] [bee] might represent the name of a "deer-bee", an insect that likes to bother and sting the animal.
While we are at it, over the centuries (in my example) the stylized picture of the bee has evolved into a square with stripes across it and two lines sticking diagonally out of the top like a rabbit-ear antenna to represent the bee’s wings; at the same time that a symbol representing a stylized picture of a prison cell window has turned into a square with the stripes without the rabbit-ears antenna, and it represents the concept "bar" or "bars" meaning "rod" or "rods", and also "chocolate bar", and the syllables /bar/ and /barz/, and by extension the words "barbarian" and "barbaric". And sometimes a scribe drawing the [bee] symbol accidentally leaves off the rabbit-ears antenna, or draws it badly so it is hard to recognize, or the inscription has become damaged; so that the [bee] symbol more or less looks like a [barred-window] symbol, even though that is not what the scribe intended. And sometimes the [barred-window] symbol grows a decoration that looks vaguely like the rabbit-ears, due to style drift. And sometimes the symbol for "television", a square with rabbit-ears and no stripes, grows one or more stripes after all, or acquires damage that looks like stripes, and sometimes the [bee] and [barred-window] symbols lose some or all of their stripes due to style drift, or the stripes become damaged so it is hard to tell if they are stripes or not.
It's amazing that anyone could read Sumerian-- I'm reminded of a Lafferty story (sorry, title forgotten) in which it turns out that the only reason people can talk to each other is that language is supplemented by telepathy. (I don't think the story explained how text could possibly work.)
Link from this discussion of how to use long boring stories to answer questions you don't feel safe not answering directly. I'm not surprised that the discussion branched to include a long interesting story.