I understand that this is a Hebrew language site, but since you mentioned it, "acelga" in both Portuguese and Spanish means "chard" and not "beet".
Chard is a type of beet, also known as silverbeet or perpetual spinach. I think you'll find that the issue here is primarily a horticultural/culinary one, rather than a linguistic one. I was often served silverbeet titled "spinach" at home. (Whether or not I could be made to eat it was another matter.) Wikipedia, though, suggest that's an Australian thing...
According to this site:
http://www.caribbeanseeds.com/acelga.htm
acelga is swiss chard.
And from here:
http://www.answers.com/swiss+chard&r=67
swiss chard is:
a) a kind of beet
b) has spinach like leaves
c) is also known as silver beet
So some kinds of beets may look like spinach.
I agree that the question is horticultural/culinary - but it definitely has linguistic implications.
My latest guess for how tered came to be spinach is that silka / salk meant spinach in Arabic, then someone read the gemara and said that therefore teradin also must mean spinach. But I have no proof of that...
Chard (bleter burik בלעטער בוריק) and beets (burikes בוריקעס) are both varieties of beta vulgaris
my guess is that silka refers to chard or beet greens and folks unfamiliar with the greens identified them as spinach.
Commenting by HaloScan
