If someone chooses to quit college, I can refer to that person as a “former” student of that college. It therefore appears that I can use alumnus according to the definitions given for that term given by the References section given below.

However, that same condition also seems to match the definitions of a dropout.

Which one should I use here: is the former student an alumnus or a dropout?

References

1. alumnus

1.1. Oxford Dictionary of English on alumnus:

a male former pupil or student of a particular school, college, or university

1.2 Oxford English Dictionary on alumnus: ^{(paywalled links)}

Inflections: Plural alumni.
Origin: A borrowing from Latin. Etymon: Latin alumnus.
Etymology: < classical Latin alumnus foster-son, (in figurative use) son or child, ward, protégé, charge, pupil < alere to nourish (see ᴀʟɪᴍᴇɴᴛ n.) + an ablaut variant (zero-grade) of the same Indo-European base as ancient Greek ‑μενος, ending of medio-passive participles.

Compare ᴀʟᴜᴍɴᴀ n.

1. † A male pupil or student attending a particular school, university, or other seat of learning. Obsolete.

2. originally U.S.

   • a. A former pupil or student (typically male) of a particular school, university, etc.; a graduate of a particular seat of learning.
     
     ^{The singular alumnus almost always refers to a male, but the plural alumni is often used to refer to graduates of either sex.}

   • b. colloquial. In extended use: a former member of any group; an ex-member of a team, band, organization, etc.

2. drop-out, dropout

2.1 Oxford Dictionary of English on dropout:

a person who has abandoned a course of study or who has rejected conventional society to pursue an alternative lifestyle

2.2 Oxford English Dictionary on dropout: ^{(paywalled links)}

2. A person who ‘drops out’ (see to drop out 2 at ᴅʀᴏᴘ v. Phrasal verbs), esp. from a course of study or from society; also, the act of withdrawing. Also attributive. colloquial (originally U.S.).

An alumnus is undoubtedly a graduate or former student of an establishment of higher education and the implication is normally that such people have completed a course of study there. Whether or not anyone who hasn’t completed a course of study is recognized as an alumnus would, I imagine, be a matter for each establishment to decide. If you wish to avoid ambiguity, dropout would be the better choice. Alternatively, you could describe the personal circumstances of academic failure in more detail. (I have used alumnus, but the feminine is alumna. The plural of alumnus is alumni and the plural of alumna, alumnae. In referring to male and female graduates, it seems to be the convention to call them alumni.)

The term alumnus/alumna refers to anyone who attended a particular university (Merriam-Webster definition). Use graduate or dropout (or non-graduate alumnus) to specify whether or not someone completed a degree.

Many tech company founders dropped out of college, but are still considered alumni. Here is a list of Harvard's non-graduate alumni on Wikipedia.