IRR calculator wrote...
Thanks for your help. I guess that I am still confused. I thought
that continous compounding was essentially another form of daily
compounding.

Nope. Continuous compounding uses force of interest. Daily compounding
only approximates continuous compounding.

Are you saying that it compounds as of each transaction date?

Yes, effectively. If you had a nominal annual rate of 4.8% compounded
monthly, that's a monthly effective rate of 0.4%. There's no
difference in result between compounding each of 3 months separately
at 0.4% and compounding the quarter at the effective rate of 1.004^3-1.