The suffix "-io-", which becomes "-ium" in accusative/nominative neuter Latin nouns, is extremely ancient. It is inherited from the common Indo-European language.

This suffix is used to derive nouns or adjectives from other nouns, where the derived nouns are understood to have some kind of relationship with the base nouns.

A great number of the names of chemical elements use the Latin variant of this suffix, i.e. "-ium", to derive the name of the element either from the name of the substance from which it has been extracted, or from the name of some characteristic property of the element or from some mythological name or from some person or place that is intended to be honored by this choice.

The name of aluminium comes from the name of the aluminium sulfate in Latin, which was "alumin-".

So "aluminium" means "something that is not aluminium sulfate, but it is related to aluminium sulfate".

On the other hand, "aluminum", which lacks the derivation suffix, just means "aluminium sulfate" (which has become "alum" in English), but the noun has been converted from the 3rd Latin declension to the 2nd Latin declension. Such conversion between declensions were not unusual even for native Latin speakers.

So this is definitely a grammar mistake, which is annoying for those who understand the meaning of words, because it creates an exception that must be remembered, instead of applying the general rule.

In general the British and American scientists have always been much more lax in observing grammar rules than the continental Europeans. So there are also other chemical elements where the English names differ from the correct names. For instance the name of the chemical element "silicium" is derived from Latin "silic-" (flint), from which it is extracted, but in English it has been changed to "silicon", for the silly reason to make it rhyme with "carbon", despite the fact that most chemical properties of silicon resemble more those of boron or of phosphorus or of germanium, than those of carbon (because valence is only 1 of the 3 main properties that determine chemical behavior, electronegativity and ionic/atomic size are equally important). (Carbon is one of the few elements that were known in pure form already in the Ancient World, so its name is not derived from another noun.) ("Boron" has also been changed in English to make it rhyme with "carbon", which is equally baseless.)