No. bootp was an earlier version of PXE but it had some limitations and difficulties to set up all the required parts. PXE was developed as a replacement for bootp with the idea to remove the earlier limitations and make setup easier.
EDIT: This link may help explain the history. https://en.wikipedia.org/wiki/Preboot_Execution_Environment
With regard to the problems of the client not finding the file I can’t help you on that as PXE is not something i have had a go at yet, although it is on my list of things to explore with my vm testbed.
I am sure that there will be other people who have experience with using the PXE/tftpd combination on IPFire and will be able to help.