Here is how Blackstone explains it as it involves aliens - and aliens are a more accurate item of discussion for our purposes:
“SIR Edward Coke50 also holds, that if an alien comes into England, and there has issue two sons, who are thereby natural born subjects; and one of them purchases land, and dies; yet neither of these brethren can be heir to the other. For the commune vinculum , or common stock of their consanguinity, is the father; and, as he had no inheritable blood in him, he could communicate none to his sons; and, when the sons can by no possibility be heirs to the father, the one of them shall not be heir to the other. And this opinion of his seems founded upon solid principles of the ancient law; not only from the rule before cited,51 that cestuy, que doit inheriter al pere, doit inheriter al fits [he who is heir to the father is heir to the son]; but also because we have seen that the only feudal foundation upon which newly purchased land can possibly descend to a brother, is the supposition and fiction of law, that it descended from some one of his ancestors: but in this case as the immediate ancestor was an alien, from whom it could by no possibility descend, this should destroy the supposition, and impede the descent, and the land should be inherited ut feudum stricte novum [as a fee strictly new]; that is, by none but the lineal descendants of the purchasing brother; and, on failure of them, should escheat to the lord of the fee. But this opinion has been since overruled:52 and it is now held for law, that the sons of an alien, born here, may inherit to each other. And reasonably enough upon the whole: for, as (in common purchases) the whole of the supposed descent from indefinite ancestors is but fictitious, the law may as well suppose the requisite ancestor as suppose the requisite descent.
IT is also enacted, by the statute II & 12 W III. c. 6. that all persons, being natural-born subjects of the king, may inherit and make their titles by descent from any of their ancestors lineal or collateral; although their father, or mother, or other ancestor, by, from, through, or under whom they derive their pedigrees, were born out of the king’s allegiance. But inconveniences were afterwards apprehended, in case persons should thereby gain a future capacity to inherit, who did not exist at the death of the person last seized. As, if Francis the elder brother of John Stiles be an alien, and Oliver the younger be a natural-born subject, upon John’s death without issue his lands will descend to Oliver the younger brother: now, if afterwards Francis has a child, it was feared that, under the statute of king William, this newborn child might defeat the estate of his uncle Oliver. Wherefore it is provided, by the statute 25 Geo. II. c. 39. that no right of inheritance shall accrue by virtue of the former statute to any persons whatsoever, unless they are in being and capable to take as heirs at the death of the person last seized: — with an exception however to the case, where lands shall descend to the daughter of an alien; which daughter shall resign such inheritance to her after-born brother, or divide it with her after-born sisters, according to the usual rule53 of descents by the common law.”
http://ebooks.adelaide.edu.au/b/blackstone/william/comment/book2.15.html
To repeat for emphasis:
“IT is also enacted, by the statute II & 12 W III. c. 6. that all persons, being natural-born subjects of the king, may inherit and make their titles by descent from any of their ancestors lineal or collateral; although their father, or mother, or other ancestor, by, from, through, or under whom they derive their pedigrees, were born out of the king’s allegiance.”
To make matters more complex, aliens were not allowed to hold property:
“As aliens cannot inherit, so far they are on a level with bastards; but, as they are also disabled to hold by purchase,47 they are under still greater disabilities. And, as they can neither hold by purchase, nor by inheritance, it is almost superfluous to say that they can have no heirs, since they can have nothing for an heir to inherit: but so it is expressly held,48 because they have not in them any inheritable blood.”
However, an alien could have property in a foreign country - for example, in the US.
The Venus is a painful case to read, but it gives an idea of the complexity that could be involved:
http://supreme.justia.com/cases/federal/us/12/253/case.html
Aliens are those who have not yet become denizens.
There should be no confusion on your part. The English-born children of aliens DO NOT have the same privileges as English-born children of English subjects. That's why Blackstone deliberately used the disclaimer, "generally speaking."
If they were the same, there would be no need for the disclaimer Blackstone used.