When using Apple Pay Are there any limits on sending or receiving money

Yes there are, and they are spelled-out in the T&C.

https://applecash.greendot.com/termsconditions/

The fundamental, overarching limitation is:

“… The Services may only be used for personal, non-commercial purposes …”

If Green Dot suspects otherwise, your account can be closed w/ little recourse.

See also:

Apple Cash and person to person payments limits - Apple Support

Are you referring to Apple Cash, Cash App or Venmo?