Definition of Neurosis
Today, neurosis (plural: neuroses) is a class of functional mental disorders involving chronic distress but neither delusions nor hallucinations (Wikipedia).
As well as other theories, neuroses play a central role in Freudian psychoanalysis (whereby all of Freud's theories are considered by many to be pseudoscientific. More can be read in my answer to this in meta).
However, the term neurosis was coined by the Scottish doctor William Cullen in 1769 to refer to "disorders of sense and motion" caused by a "general affection of the nervous system." Cullen used the term to describe various nervous disorders and symptoms that could not be explained physiologically.
According to C. George Boeree, professor emeritus at Shippensburg University, the symptoms of neurosis as described today may involve:
... anxiety, sadness or depression, anger, irritability, mental confusion, low sense of self-worth, etc., behavioral symptoms such as phobic avoidance, vigilance, impulsive and compulsive acts, lethargy, etc., cognitive problems such as unpleasant or disturbing thoughts, repetition of thoughts and obsession, habitual fantasizing, negativity and cynicism, etc. Interpersonally, neurosis involves dependency, aggressiveness, perfectionism, schizoid isolation, socio-culturally inappropriate behaviors, etc. (Wikipedia & Boeree, 2002).
As for any declination of use for the term neurosis mentioned by @AliceD in his answer, although people are not generally labelled as suffering from a neurosis or even a psychosis, neurosis is as pointed out, an umbrella term for a range of mental health problems and is different to psychoses — another umbrella term.
In fact the current version of the Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition (DSM-5) talks of neurotic disposition and neuroticism within certain mental health problems, e.g.:
Behavioral inhibition and neurotic disposition (i.e., negative affectivity [neuroticism] and anxiety sensitivity) are closely associated with agoraphobia but are relevant to most anxiety disorders (phobic disorders, panic disorder, generalized anxiety disorder). Anxiety sensitivity (the disposition to believe that symptoms of anxiety are harmful) is also characteristic of individuals with agoraphobia.
The terms neurosis and neurotic are also used in the ICD-10 (2016) Chapter V F40–48.
Definition of Psychosis
A psychosis (plural: psychoses), as mentioned before, is an unberella term for a range of mental health problems. A psychosis is an abnormal condition of the mind that results in difficulties telling what is real and what is not. Symptoms may include false beliefs and seeing or hearing things that others do not see or hear. Other symptoms may include incoherent speech and behavior that is inappropriate for the situation (Wikipedia & NIMH, n.d.).
From your research, you deduced that
psychosis is brought about particularly by the use of alcohol and illicit use of drugs and their withdrawal.
Use of alcohol and illicit use of drugs and their withdrawal does not only create psychoses, but can instead cause a neurotic mental health conditions such as anxiety or depression (American Addiction Centers).
Sometimes, mental health problems can cross the devide both ways between Neuroses and Psychoses.
Take for example below:
Table put together in my notes whilst training
* Although BPD, Bipolar Disorder and PTSD are generally neuroses, they can involve psychotic episodes in some cases.
Psychotic episodes in PTSD can involve flashbacks (the sense of being back at the traumatic event) through hallucinations affecting touch, taste, smell, sound and sight either affecting one of the senses or a combination of them. Bipolar clients (Mind, 2018) can experience visual or auditory hallucinations. Note: I have just noticed webpage linked to at Mind has been updated since I wrote my training notes and the link here is kept for completeness of information on Bipolar Disorder. Information on psychotic episodes can be found by clicking the bipolar moods and symptoms link on the page.
Psychotic symptoms can include:
- delusions, such as paranoia
- hallucinations, such as hearing voices
Not everyone with a diagnosis of bipolar disorder experiences psychosis, but some people do. It's more common during manic episodes, but can happen during depressive episodes too. These kinds of experiences can feel very real to you at the time, which may make it hard to understand other people's concerns about you.
(See our pages on psychosis for more information.)
Boeree, C. G. (2002). A Bio-Social Theory of Neurosis. Shippensburg University [Online]
Retreived from: http://webspace.ship.edu/cgboer/genpsyneurosis.html
Mind, 2018. Bipolar Disorder. [Online]
Retreieved from: http://www.mind.org.uk/information-support/types-of-mental-health-problems/bipolar-disorder
NIMH (n.d.). RAISE Questions and Answers. NIMH [Online]
Retreived from: https://www.nimh.nih.gov/health/topics/schizophrenia/raise/raise-questions-and-answers.shtml