First the usual caveat: I'm going to mention a few bits of law here that are almost certainly specific to the US. It almost certainly doesn't apply at all outside the US.
In my opinion, your first example is almost completely meaningless, at least as far as affecting what a court is likely to decide about your patent. It's simply stating what's essentially a fact of patent law, already well known to any judge who's at all competent.
Giving more specific alternatives in the specification, such as in your second example, can have considerably more effect. This is especially true if your claim is written as a means + function limitation (wording like "means for X"). The supreme court has ruled that such a limitation is so general that it cannot/should not be taken literally as covering any possible means for carrying out the specified
X. Rather, it is to be treated as a reference to the specification, and those means cited in the specification for doing
As such, if you have a claim limitation like "means for storing data", and the only storage listed in your specification is a hard disk drive, then the proper reading of the claim is that "means for storing data" that should be treated as literally meaning "a hard disk drive." On the other hand, if your specification lists alternatives such as "hard disk, ROM, Flash, or CD-ROM", then the literal meaning of "means for storing data" would be "hard disk, ROM, Flash, or CD-ROM", within the scope of that patent.
By contrast, an apparatus claim that included (for example) "a data storage device" as a limitation should not be limited in the same way. In such a case, it would (probably1) be proper to construe any of the above storage devices as falling within the literal meaning of "a storage device", even if the only storage device cited in the specification was a hard disk.
That said, I should add that the patent specification is also properly treated as a source of definitions of terms used in the claims, if the meaning of those terms is not clear from the claims themselves. As such, if a claim uses a term that would not have been known to a person of ordinary skill in the art at the time of the invention, then it's perfectly correct to look to the specification to see if the specification defines that term -- and if so, the definition within the specification should prevail over definitions from external sources.
I should probably also add that it's not always obvious whether a limitation is really a means+function limitation or not. For example, a few years ago there was a case where a claim used the phrase (going from memory here) "perforating means". Based on the subject matter, it was pretty clear that this really referred to something like "perforations", not something like "a machine for producing perforations." In any case, the patent specification cited not only perforations, but a number of other methods of weakening material along a line to provide a place that was easy to tear. The case went (at least) as far as the Court of Appeals for the Federal Circuit, with the only real disagreement being over whether "perforating means" qualified as a means+function limitation or not. Even within the CAFC, the decision on that wasn't unanimous. They decided it was a means+function limitation, but Judge Rader wrote a dissenting opinion.
1. "probably" hinting at the possibility that it depends on the subject area of the patent. For example, if the patent were about individual cells in a DRAM chip, "data storage device" might mean something like "a capacitor".