differentiating between all that and what

Original (extracted from the book The Scarlet Letter):

Like all that pertains to crime, it seemed never to have known a youthful era.

My own rephrased sentences:

Like whatever that pertains to crime, it seemed never to have known a youthful era.

Like what pertains to crime, it seemed never to have known a youthful era.

Could you throw a light on the difference between the bolded parts of the sentences above? Or could you give me a vivid explanation or example? Or explain the difference in meaning of the sentences?

Like all that pertains to crime, it seemed never to have known a youthful era.

This sentence says a couple things. It says that everything that pertains to crime seems to have never known a youthful era. It also says that 'it' (a wooden jail, apparently?) is a member of this class of things, and that therefore 'it' also seemed to have never known a youthful era.

Logically:

Let C be the set of things that pertain to crime.
Let Y be the set of things that seem to have never known a youthful era

For any x,
x ∈ C => c ∈ Y

Let p be 'it'
p ∈ C

Therefore, p ∈ Y

Your first phrasing has an extraneous 'that'. Ignoring the extra 'that', your sentence is logically equivalent. However, 'whatever' is less formal and sounds less precise than 'all that'. It has the same meaning, but it doesn't sound as good.

I think your second phrasing fails to capture the idea that everything that pertains to crime has this property. It also sounds strange: "what pertains to crime" is the phrasing you would use to ask what things are in this set, not the phrasing you would use to indicate that you're talking about all the things in the set.

Here are some alternative phrasings that come closer to the original sentence:

Like everything (that pertains)/pertaining to crime...

Like all things (that pertain)/pertaining to crime...

Like anything (that pertains)/pertaining to crime...