Information that's available to the public is excluded from export controls.
The ITAR defines "public domain"(§120.11): “Public domain means information which is published and which is generally accessible or available to the public”. Public domain information is excluded from control as ITAR technical data.
EAR part 734.3(b)(3) refers to “publicly available technology and software”, and does not use the expression "public domain". Publicly available technology and software are excluded from control under the EAR — except 5D002 encryption software (although 5D002 object code whose corresponding source code is publicly available is considered to be publicly available).
These share the idea that publicly available information should not be subject to export controls. They differ in how it can be made publicly available. Information in the scope of the ITAR can be made publicly available only by the means described in §120.11, or with the explicit authorization of the State Department. Information in the scope of the EAR can be made publicly available by a person who is not restricted from doing so — as they might be sue to a non-disclosure agreement for proprietary information from a commercial sponsor, or ia distribution restriction for government-funded research.
Another meaning of "public domain" is a work whose intellectual property rights (copyright, patent, trademark) have expired (or never existed). This is different — for example a piece of software can be copyrighted (so not "public domain" from an IP perspectice) but published and generally accessible (so "public domain" from an export control perspective).
"Open source" isn't "public domain" in the IP sense, because it typically has an owner who provides it, often free, under a license granting a wide range of rights and obligations to the user. But it can be "public domain" from the export control perspective.