Learn English – term for words that have identical singular and plural forms

This question is actually quite broad. Irregular plural forms can arise for a variety of reasons. Wikipedia has a huge section on the subject, with six subsections: "Nouns with identical singular and plural", "Irregular -(e)n plurals", "Ablaut plurals", "Irregular plurals from Latin and Greek", "Irregular plurals from other languages", and "Words better known in the plural".

Wiktionary has a list of English nouns with irregular plurals.

Lastly, there are nouns that (depending on context) can be countable and uncountable, e.g. water, cheese, or email.

Etymonline has this to say:

-ics
in the names of sciences or disciplines (acoustics, aerobics, economics, etc.) it represents a 16c. revival of the classical custom of using the neuter plural of adjectives with -ikos (see -ic) to mean "matters relevant to" and also as the titles of treatises about them. Subject matters that acquired their names in English before c.1500, however, tend to remain in singular (e.g. arithmetic, logic).

So yes, at some point in history, there were such things as physic (meaning "natural science"), mathematic (meaning "mathematical science"), etc. that were later turned into plural forms but kept being treated as singular.

Edit: having looked in a few more places, it appears that in contemporary English, it still makes some sense to have both the suffix -ic and its plural form -ics. According to the Collins English Dictionary, the former has kind of specialized in forming adjectives, while the latter is happily forming nouns:

-ic
suffix forming adjectives

1. of, relating to, or resembling: allergic, Germanic, periodic. See also -ical.
   [...]

[from Latin -icus or Greek -ikos; -ic also occurs in nouns that represent a substantive use of adjectives (magic) and in nouns borrowed directly from Latin or Greek (critic, music)]

[...]

-ics
suffix forming nouns (functioning as singular)

1. indicating a science, art, or matters relating to a particular subject: aeronautics, politics
2. indicating certain activities or practices: acrobatics

[plural of -ic, representing Latin -ica, from Greek -ika, as in mathēmatika mathematics]

The key here is that they are not just two unrelated suffixes. Much rather, one is etymologically a plural form of the other. As the American Heritage Dictionary succinctly puts it, -ics is "-ic + -s".