I've read your post a half dozen times and can't figure out much from it. Perhaps if you attached your sheet, it would provide much of the explanation.

As for "excluding the date", you can format dates and times to display in myriad ways. But the underlying data in the cell is always a floating point number where 0 is midnight on 1/1/1900 and each day thereafter adds 1. Fractions of days are decimals, an hour being 1/24, a minute being 1/(24*60), etc.

So you can display just the time in those cells, but when you type in the data, your calculations won't work if the times span two days unless you explicitly enter the times as such. If you just enter 23:19 and 0:15, Excel will enter both as those times on the same day, 1/1/1900, and the calculation will return 23 hours and 4 minutes.

Properly subtracting the later time from the earlier...

[7/2 00:15] - [7/1 23:19] = 0.038889

This is the fraction of one day that the difference of those times (56 minutes) is.

56/(24*60) = 0.038889