I've just spent 2 hours sorting through various references to group selection to try to figure out whether your distinction is correct. As Samir Okasha writes, "The group selection debate has been characterised by perennial disagreements over concepts and terminology, as well as empirical fact."

So far, Stephen J. Gould uses this group/species distinction, and almost everyone else rejects it. The more common usage is given in the BioTech Life Science Dictionary:

Group selection: A type of natural selection which acts upon whole groups rather than on individuals. Group selection includes interdemic selection (acts on populations within a species) and species selection (acts on species within a higher taxon).

(Gould uses the term interdemic selection, but says it is synonymous with group selection, and distinguishes it from species selection.)

Eliezer's post talked about species selection. David Wilson's 2009 blog series on group selection, Truth & Reconciliation (linked to in the post), says nothing about any distinction between "group selection" and "species selection"; and the endangered bird species example of group selection in part 18 (p. 39) is species selection. Read the Wikipedia entry on group selection - everything that it says applies to species selection. All of the arguments presented against group selection apply equally to species selection. Some of the instances of group selection it provides are species selection. It never draws any distinction between group selection and species selection.

Many examples in various sources of group selection do not have between-group migration, and do have extinction of groups. For example, the ant colonies that EO Wilson talks about - there is AFAIK no gene transfer between ant colonies, since ants can't migrate from one colony to another. On the Wikipedia page on group selection, it includes as examples viruses in rabbits, where selection occurs at the level of a single rabbit, and no gene transfer occurs between different infected rabbits.The Rauch et al analysis referred to is a similar case. So is the "brain worm" example.

Many attacks on group selection, including Williams' Adaptation and Natural Selection (1966), speak in general terms about selection at higher levels indiscriminately, not singling out group vs. species selection. Here is what Richard Dawkins writes when attacking group selection in The Selfish Gene:

[A] group, such as a species or a population within a species, whose individual members are prepared to sacrifice themselves for the welfare of the group, may be less likely to go extinct than a rival group whose individual members place their own selfish interests first. Therefore the world becomes populated mainly by groups consisting of self-sacrificing individuals. This is the theory of 'group selection', long assumed to be true by biologists.

Here is a quote from Samir Okasha (2005), Maynard Smith on the levels of selection question:

Thus in a 1976 review of the subject, [JMSmith] argued that group selection ‘‘requires that groups be able to ‘‘reproduce’’, by splitting or by sending out propagules, and that groups should go extinct’’ (1976, p. 282). The process envisaged by Wynne-Edwards, in which reproductively isolated demes give rise to other such demes, satisfies these conditions, Maynard Smith argued, as does the process of species selection as described by Gould and Eldredge, in which speciation plays the role of demic reproduction."

So, George Williams, John Maynard Smith, Richard Dawkins, and David Wilson all agree that group selection includes species selection.

Maynard Smith's haystack model, which was the original theoretical basis for rejecting group selection (and is fatally flawed; see p. 17 of the David Wilson T&R essay), does not work on species selection. The mathematical model that Eliezer used does not apply to species selection (nor to interdemic selection in general). Yet they use the phrase "group selection". So there is some basis for considering group selection to be synonymous with interdemic selection; but that basis appears to be the carelessness of earlier theorists.

The group-selection-bashing I've witnessed for decades has always taken the line that all group selection, including species selection, is equally bad. I've seen many people object to the invocation of group selection, and I've never noticed any of them draw a distinction between interdemic and species selection.

Please cite a reference for your usage of the terms.

As a result, species selection isn't very controversial - compared to group selection.

Wikipedia seems to contradict this: "It remains controversial among biologists whether selection can operate at and above the level of species."

I did a quick search on Google and found a paper from 2010 which claims that "Species selection as a potential driver of macroevolutionary trends has been relegated to a largely philosophical position in modern evolutionary biology."

I'm not very familiar with biology, but at a glance it looks like species selection is pretty controversial.

That may be so. If so, I am misusing the terminology. But if so, other people routinely use the objection to what you are calling "group selection" to rebut invocations of what you are calling "species selection".