The young scientist asks:
“What is the correct definition?”.
The old scientist answers:
“As is often the case in biology, there is no correct definition — different people adopt different usages.”
This answer attempts to explain why this is the case and how to find out other than asking people who despite greater age and knowledge, may be mistaken in their dogmatism.
Often in biology a term is coined for a new observation or concept that has arisen from scientific research. Subsequently further research reveals new aspects or details. These expand rather than negate the original discovery, but can make original definitions inadequate. Individual scientists modify the terminology, and naturally do so in relation to their own concerns, which may differ from those of other scientists. Hence different usages arise.
One might have expected that there would be committees of scientists to lay down rules, but this tends to be confined mainly to the physical and chemical sciences where precise common terminology is important. Because modern biology is fast moving, people are inclined to either wait until the dust has settled (e.g. in enzyme nomenclature) or let “terminological Darwinism” take its course.
I am not really a biologist in the traditional sense, so I lacked any dogmatic attitude to the question, and, instead made Wikipedia my first port of call. This is not a definitive authority on anything, as anyone can edit it. However in this case it is, I think, useful. Under History we read:
The term was introduced by Rudolf Bon Kölliker in 1863, originally as a synonym for protoplasm, but it later has come to mean the cell substance and organelles outside the nucleus.
There has been a certain disagreement on the definition of cytoplasm as some authors prefer to exclude from it some organelles, especially the vacuoles and sometimes the plastids.
Further in the article there is a reference to the term cytosol which is used in an experimental (rather than an observational) sense to refer to the portion of the cytosol from which membranous organelles have been removed.
The date 1863 is worth noting as it is before the discovery of organelles such as the mitochondrion (1880), and knowledge of others at the time was at a primitive stage.
Addendum: Advice to the young scientist
You have eaten from the tree of knowledge and have lost your innocence. Cry a tear then wipe it dry, as you did when you realized there was no Santa Claus. If you wish to become a scientist or even just to understand science you must understand how science works.
Do not reproach your teachers. They are fallible because they are human. Be charitable towards them as you would have them be to you.