Usage as verbs
The population of Italy has decreased in recent years.
The population of Italy has reduced in recent years.
In this example “decreased” is correct. This is because nobody is making Italy’s population get smaller – it is just happening naturally. In this sentence “decreased” works as an intransitive verb. An intransitive verb is one that does not require an object. It is enough to say “something decreased”.
In contrast, “reduce” is a transitive verb. It needs an object. You cannot say “something reduced”; you must say “something reduced something”, where the second “something” is the object of the sentence. E.g.:
The epidemic reduced the town’s population by several thousand.
“Decrease” can also work as a transitive verb, however, so it is also correct to say:
The epidemic decreased the town’s population by several thousand.
Transitive verb (the object is “costs”)
By switching to the automated billing system, we have managed to significantly reduce / decrease costs.
Intransitive verb (no object)
Costs have significantly decreased / reduced since we switched to the automated billing system.
Transitive verb (the object is “the numbers of people”)
The COVID-19 pandemic reduced / decreased the numbers of people travelling by plane by an enormous amount.
Intransitive verb (no object)
The numbers of people travelling by plane decreased / reduced by an enormous amount due to the COVID-19 pandemic.
One way of thinking about the difference between these verbs is as follows:
reduce means “to make smaller”
decrease means “to become smaller” as well as “to make smaller”.
You may also replace these verbs with “cut” or “fall”. If you cut something you reduce it; whereas if something falls it decreases.
The government has cut / reduced the top rate of tax.
By switching to the automated billing system, we have managed to significantly cut / reduce costs.
Costs have significantly fallen / decreased since we switched to the automated billing system.
Revenues have fallen / decreased due to lower demand for exports.
“Diminish” is not used as often as “reduce” or “decrease”. It is more similar to “decrease” as it works as both a transitive and intransitive verb – meaning, respectively, “to make smaller” and “to become smaller”. For example:
The recent rains have diminished the threat of drought. [reduced and decreased would also work here]
The nation’s gas reserves are diminishing rapidly. [decreasing would also work here]
Usage as nouns
Reduction is the noun.
Decrease is the verb and the noun.
Although diminishment and diminution do exist, they are very rare, and I do not recommend using them.
The government’s proposed tax reductions / decreases have unsettled the markets.
Lower demand for exports has led to a reduction / decrease in revenue.
We have seen a significant reduction / decrease in costs since we switched to the automated billing system.
Note that reduction has another well-known meaning. In chemical reactions, reduction is the gain of electrons (while the opposite, loss of electrons, is called oxidation). The verb reduce can also be used in this context.