Double added idiom

No, they don't have the same meanings. And the idiom "cry-baby" is not remotely like the text that cllaims to illustrate it.

In fact it's rather hard to see how a verb phrase (eg "cry ones eyes out") could be thought to mean the same as a compound noun (eg "cry-baby"). In fact they don't mean the same thing at all.
The confusion has probably arisen because the idiom labelled "cry-baby" isn't "cry-baby" at all, but "cry like a baby".
The three idioms in this confusion are:
Cry like a baby: means cry with tears and loud wailing noises and without words.
Cry ones eyes out: means weep continuously with many tears for more than a short time.
Cry-baby: means a person who weeps and moans often, frequently as a result of something trivial which no reasonable person would consider a cause for weeping and moaning.

Done.

I don't want to make any mistakes.

Please merge:

There's/That's the rub
https://lyricstranslate.com/en/theresthats-rub

There’s the rub
https://lyricstranslate.com/en/there%E2%80%99s-rub

Thanks in advance.

I hear "There's no smoke without fire" far more often that "Where there's smoke there's fire" - in fact I've heard the latter about as often as I've heard "Là où il y a de la fumée il y a du feu" (hardly ever). Is this perhaps a difference between Brit English and American English? Or even between different communities withing Britain?