The '%' symbol is simple syntactic sugar, it's to be read as the fraction "/100" just as '' is for "/1000". When you write 38%, you write 38/100 or 0.38 and nothing else.
Gruber corrected his error (as visible in the first post you quoted in this thread *) and now makes sense. Yes, it was language problem, and he corrected to express what he wanted [* but it looks like he reverted back to the original version of his post now, as corrections aren't visible anymore, eh].
Yes, 138 is equal to 1.38 times 100, but something 138% larger than the reference is 238% as large. And so 138 is 38% larger than 100, not 1.38 times larger.
But then your second sentence doesn't make sense because you just wrote it the sentence before.
Yes as you say, its a language problem.
Again, something "1.38 times larger" is not what you want to mean: you mean "1.38 times as large".
Yes, "1 time larger" means the same as "2 times as large".
Ha ha, quite right! The problem comes when using "times larger," which is incremental, and "times as large," which is absolute.
In everyday language, as you can see they are often used interchangably, which is where confusion ensues