Learn English – Word order in defining and non-defining relative clauses

The authors themselves say of the traditional terms:

They are misleading: the integrated relative is NOT always restrictive, in the sense of picking out a subset of the set denoted by the head noun.

They go on to give supporting examples. However, if you’re familiar with the CGEL, you probably already know this.

As Janus Bahs Jacquet states in the comments, the difference is essentially one of formality. The Cambridge Grammar of English states the following general principle:

In a wide range of informal styles, that is used instead of who/whom or which in defining relative clauses. (p571)

This principle is confirmed by Swan in Practical English Usage:

We often use that instead of who or which, especially in an informal style. (p478)

Swan goes on to note:

That is especially common after quantifiers like all, every(thing), something, any(thing), nothing, little, few, much, only, and after superlatives. (p478)

When the relative reference is to a person, Swan states:

That is often used in identifying relative clauses instead of who/whom/which. That is most common as an object or as a subject instead of which. That can be used as a subject instead of who, but this is quite informal. (p482)

The Cambridge Grammar of English notes (of defining/identifying relative clauses):

That may refer to the complement of a preposition, but not when the preposition is placed immediately before the relative pronoun:

• The other girl that I told you about also lives in Bristol.

So, the following is not grammatical:

The other girl about that I told you also lives in Bristol.

It must be: ... about whom ... . Of course, this very formal usage conforms to the general principle noted above.