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According to this,
[辛い]{からい} means both spicy and salty. Where I live we associate spicy with pepper, not salt.
Is this something similar to the case of "ao", meaning both green and blue? (or something in between them).
Are there words for differentiating foods with too much salt than foods with too much pepper?
Yes, this is similar to 青 meaning green.
からい in modern standard Japanese almost always means spicy, but in the old days this word safely also meant salty. But somewhere in the past (most) Japanese people noticed spicy and salty are clearly different concepts, and started to use a different word for the latter; it's simply 塩辛い. (しょっぱい is another term for salty things.) (This story was not very strict. からい in archaic Japanese primarily meant salty, but as this word gained the meaning of spicy, a different word, 塩辛い, was made and assigned to the original meaning. A similar thing happened for かわいい.)
I remember my grandmother, who was born in the 1920's in a rural area of western Japan, often used からい for salty things, and she was also a person who often used 青い for green things.
から・い【辛い／×鹹い】
１ トウガラシ・ワサビなどのように、舌やのどを強く刺激するような味である。「インド風の―・い料理」→五味 (ごみ)
２ （鹹い）塩気が多い。しょっぱい。「―・い煮つけ」⇔甘い。
(辛い read as つらい means a totally different thing, and it happens to be close to salty as in "salty experience", but I don't think it's important now.)
Apparently, in some dialects, 辛い and 塩辛い are still not distinguished in daily life.
関西の方は「しょっぱい」ことを「からい」ということについて
京都市で生まれ育った者です。
ご指摘のとおり、私は「辛い」と「塩辛い」は言葉の上で区別しません。どちらも、「からい」です。おそらく周りの者もほとんどがそう話すように思います。意味は、既出のとおり文脈で判断します。ややこしい時は、「塩辛い」ということ？、というふうに確認し合うわけです。
According to this, 辛からい means both spicy and salty. Where I live we associate spicy with pepper, not salt.
Agreeing with what @siikamiika stated, it could be a misrepresentation of 辛い【つらい】, but considering the dictionary you used was an English one, "Salty", in this case, can also refer to an upset person, in English terms.
So this sentence, given by the reference you provided with the meaning "salty":
彼女は多くの辛い思いを経験してきた。She has gone through many difficulties.
Could refer to her "upset" state referring to her experiences, or if replaced with 辛い【つらい】, her "painful experiences".
However, I am not certain that "salty" (in terms of emotion) in English, can also be 辛い 【からい】 in Japanese. 辛い【つらい】 makes more sense.
Are there words for differentiating foods with too much salt than foods with too much pepper?
There are phrases, but not specific words. However notice that salt (塩) is used along with 辛い.
Too much salt: 塩が辛い or おお塩辛い
Too much pepper: コショウを入れすぎた
I'd use 塩辛い when something is salty.
BTW, 激辛（gekikara) only means "extremely hot/spicy." We never say 激辛 for "very salty."
We call "too salty" 塩辛すぎる, とても塩辛い or 塩気が強すぎる（shio-ke ga tsuyo- sugiru）.
