I have an Arab friend who is an expert on Islamic banking and finance (which is intimately connected to Islamic legal thinking), so I asked him to help me out with the question I just asked. Here is his answer. Please note that it is one answer (he says "I have argued" which is a sure sign he means that his answer is his considered opinion and that there is some controversy here...fyi).

Hello Nat:

I have argued that practical Islamic jurisprudence (fiqh) has in fact been common-law like. The reason for lack of transparency, however, is that the rhetoric of Islamic law sounds as if it is an immediate interpretation of a canon law (Shari`a). To add to confusion, most Arab countries have secular civil codes, adapted from French and Swiss codes, and that has shaped their understanding of Islamic law as well.

Let me see if I can make the terms clear to you:

* Shari`a is the Arabic equivalent of the Jewish Halakha, an all encompassing code for life. It includes things such as honor, etc., which far exceed "law" in the narrow sense.

* Authors are often careless re the distinction between Shari`a and Fiqh. The formal legal definition of Shari`a refers to revealed, immutable Law (capital L), as present in the Canon consisting of the Qur'an and Prophet Tradition. Fiqh literally means "understanding", i.e. the application of the Law to a specific instance, which requires going through multiple stages: (1) understanding the issue, (2) legal framing of the question, (3) application of the Legal (capital L) principle to the specific event.

* It is very common for people to usurp Divine authority, as it were, by using the term Shari`a for matters that are really issues of fiqh. Legal scholars distinguish between the two by saying that Shari`a is immutable, but that fiqh, exercised through the two channels of qada' (court rulings) and fatwa (scholarly opinion), varies by time, place and circumstance. When you call your preferred policy an application of Shari`a, it sounds more authoritative, and makes it more difficult for others to argue against your position.

* People who use the term "Islamic law" often mean Shari`a, rather than fiqh. Unfortunately, Shari`a is consistent with many different interpretations, and there has not been a coherent codification of Islamic fiqh since the fall of the Ottoman Empire. That is why British courts twice dismissed provisions of applying Shari`a in contracts, since they concluded that different scholars will interpret Shari`a provisions differently for the cases before them, and "Islamic law" did not qualify as the law of a sovereign nation and therefore could not be applied based on the Rome convention.

I like the writings of Wael Hallaq, but they are a bit involved.

The book that best compares Islamic law to Anglo-American common law, as you requested, would be Lawrence Rosen's The Justice of Islam, Oxford, 2000.

A good text for western audience is Bernard Weiss's The Spirit of Islamic Law, U. Georgia Press, 1998.

I hope that this helps.
I'm afraid that this more or less confirms what I thought from my own reading. Different writers use these terms in varying ways, so we're stuck with paying attention to context and not expecting too much consistency of usage across authors.

Also, it sounds like we should be a little suspicious of claims that something is a matter of Shari`a, as my pal suggests that such claims are frequently little more than a rhetorical device.