Is there a difference between “vice”, “deputy”, “associate”, and “assistant” as descriptive job titles?

Vice refers to the one who is next in command! And its usage is usually confined to a small number of people, whereas Deputy also refers the same but it is confined to considerably large number of people.

For example: There would be just one or two vice presidents under a president! On the contrary, there can be many deputy engineers under a manager.

Associate refers to someone who is usually not as high in the cadre as Deputy/Vice but of someone who is of equal level in being a sub ordinate & Assistant being the least in the cadre of the above mentioned!

So if you are looking to differentiate, it would be something like this,

Vice = Deputy > Associate > Assistant

'Deputy' literally means someone who can act in the stead of his/her superior. Hence, the verb to 'deputize' for somebody, to take their place. A sheriff's deputy is a good example.

Similarly, 'vice' comes from the Latin meaning 'in place of'. We have the familiar example of the President of the United States of America, and his/her Vice President who, while being subordinate, may take on the role of President in certain circumstances.

I would rank both 'deputy' and 'vice' ahead of 'associate' and 'assistant'. 'Associate' is commonly used to refer to general employees of not especially high rank, such as associates in a law firm. 'Assistant' is a term which can be used to mean something like 'helper' or 'aide' - it may even be pejorative depending on context - but in some cases can be used to indicate a rank similar to 'deputy', such as Assistant District Attorney, or Assistant Coach.

In general, these are quite fluid terms depending on the setting in which they are used.