What is the difference between Missing at Random and Missing not at Random data?
Definitions of missingness process are tricky.
Missing completely at random occurs when the missingness is really at random (MCAR; e.g. when conducting a survey there are error in the data entry process).


Missing at random (MAR) occurs when the missingness is not really at random, but when it could be considered at random conditioning on what is observed in the rest of the data (e.g. males are less likely to express their opinion in a survey but this is completely not related to their attitude as customers).
Missing completely at random occurs when the missingness is really at random (MCAR; e.g.
when conducting a survey there are error in the data entry process).
Missing not at random (MNAR) occurs when the missingness depends on the value of the variable (those who buy more tend to not answer survey questions).


I think that it is difficult to figure out in what category are your missing data patterns. In your case seems to me that MAR is a reasonable assumption (which is impossible to test statistically) and that multiple imputation with chained equations could be an option (mice or miceadds in R).

If you adopt a mice approach, a crucial part in the application is to carry out sensitivity analyses. what happens if you:
- impute only some of your missing data pattern?
- vary the number of imputed sets
- perform a complete case analysis.