When you write "an abstraction is a general interface to a concrete thing that allows you to substitute different but similar concrete things without changing the consumer of those things", I feel you are actually describing a module created by making use of abstractions.
Abstractions almost always represent data differently than as it is in its most concrete form (e.g. lists and trees are abstractions both often built of vectors and pointers), but that is not the purpose of abstraction. To continue with the original example, the representation of text as a sequence of lines is a sort of abstraction, but rarely the most useful one: words, sentences, paragraphs and/or syntax trees are often what you want, and they are useful because they give us a representation of the raw text that is aligned with its purpose, not because we can implement them in multiple ways.
Furthermore, while we want to do some information hiding when implementing these abstractions (think particularly of syntax trees), that is not the purpose of having these abstractions - what we are hiding is the infrastructure to make it work, not any information conveyed by the text itself.
Abstractions almost always represent data differently than as it is in its most concrete form (e.g. lists and trees are abstractions both often built of vectors and pointers), but that is not the purpose of abstraction. To continue with the original example, the representation of text as a sequence of lines is a sort of abstraction, but rarely the most useful one: words, sentences, paragraphs and/or syntax trees are often what you want, and they are useful because they give us a representation of the raw text that is aligned with its purpose, not because we can implement them in multiple ways.
Furthermore, while we want to do some information hiding when implementing these abstractions (think particularly of syntax trees), that is not the purpose of having these abstractions - what we are hiding is the infrastructure to make it work, not any information conveyed by the text itself.