Your calculation assumes that all months average exactly 30 days in length. This is not the case!
In the example given, this issue is probably not that the calculation throws up a discrepancy of about 1.6% between two different ways of calculating the difference between dates: my concern is that you seem to be saying that there is a hard stop to the project in 4 years time. How have you reached that conclusion? It sounds too like you have based this on an assumption rather than knowing what the deliverables are and how they all fit together into a planned set of activities and actions - unless the project is something to do with something that is happening on that specific date. In which case, the issue is not the number of months, but rather how many resources you may need to deploy (and hence the costs you need to incur) to deliver on that date.
If, however, the discussion is about payment for the work, then it is down to clarification of the commercial arrangements. If you are paid by the month, regardless of length, then February (28 days) is a good month, and March is less good (31 days). If you are paid by the day, then the number of months doesn't matter. Either way, get it agreed and documented, and move on.