I know the issue of inviting to a bris as opposed to just informing.
Why is there no issue when inviting to a Pidyon Haben?
The source of this minhag is based on the Rema Y:D 265-12, based on Pesachim 113b, that a person that doesn’t sit with a chabura of mitzvah is in niduy to shomayim. Rashi and Tosefos (114a D:H V’ain) explain that this is referring to eating from a seudas bris or a wedding of a kohenes to a kohen. The Pischei Teshuva Y:D 265-18 therefore says that it is preferred not to invite to a bris meal. This idea, (to be careful not to even explicitly invite) is novel and therefore we apply it only to places that we are specifically told to do so. It doesn’t even apply to a wedding, see in the first place see Igros Moshe O:C 2-95 D:H V’af. There are numerous aspects why a bris is special, i.e. because it makes a person part of klal Yisroel etc. However I haven’t seen anything specific why this aspect doesn’t apply to pidyon haben. It could be that a seudas bris is special as Rabeinu Bachya ( Parshas Lech Lecha, and and Kad Hakemach) says that a bris milah is like bringing the child as a korban, and the seuda is like eating from the meal of a korban, but this is only speculation.