I think both terms should be fine to refer to monks' going for alms
round.
The term piá¹á¸acâra is undoubtedly correct. It is found in
verses in Suttanipâta (Sn72, 137) and Apadâna (Ap 24,201, 272,
516) where it comes with verbs of car root. More can be found in
commentaries where it is used more with verbs of gam root.
As Bryan explains, the term piá¹á¸apâta is used mostly in the
sense of alms food. But in the compound
piá¹á¸apâta-paá¹ikkanta which is found frequently in the
Pali canon to refer to monks returning from alms round, I think the word
piá¹á¸apâta can have an extended sense of going for alms round
too.
It is interesting to note that Pali canonical texts refer to monks who
routinely go for alms round only as piá¹á¸apâtika, except in
the Vinaya-piá¹aka where both piá¹á¸apâtika and
piá¹á¸acârika are used perhaps interchangeably. This seems to
reinforce the idea that the term piá¹á¸apâta can refer to the
act of going for alms round too; for if it only refers to alms food, the
compound piá¹á¸apâtika may refer to any monk in the sense of
'one who depends on alms offering', which contradicts its usage in the
Pali canon.
Hence, it seems to me that both piá¹á¸apâta and
piá¹á¸acâra can be used interchangeably to refer to monks'
going for alms round. It may be interesting to note also that a
Gândhârî ms has 'piá¹á¸acâra-paá¹ikkanta' instead
of 'piá¹á¸apâta-paá¹ikkanta' as found in the Pali canon.