How to find the date differences in terms of days?

Did you read the whole article?

I quote:

"The returned time period is measured starting from the "zero date", which is 12:00 AM, December 30, 1899. However, if the period is less than one day, then the date portion is omitted. Besides, if your locale uses the 12-hour clock notation, the resulting value is displayed using "before noon" and "after noon" abbreviations (like AM/PM in English).

Because of these reasons, using the common aqConvert.DateTimeToStr method to display the TimeIntervalresults could yield quite odd results (like 12/31/1899 12:00:05 AM when the difference is 1 day and 5 seconds). This could be rather confusing for the values that reflect time duration. To avoid misunderstanding, it is better to use the dedicated method, TimeIntervalToStr, that returns a string in the D:HH:MM:SS format, which indicates the time passed since the "zero date"."

So... change your code to the following:

I tried this.
var currentdate = aqDateTime.Now();
var newDate = aqDateTime.AddDays(currentdate,3);
 
var res = aqConvert.TimeIntervalToStr(aqDateTime.TimeInterval(currentdate, newDate));

Log.Message('The interval is ' + res);

If you specifically want to peel out the days only, use res.split(':') to return an array of the string where the first element in the array is the number of days.