6 months ago I presented a talk describing some research I had been doing and presenting some half finished results. Ive since discovered that one of the attendees took my idea from the talk and decided to pursue the same research project, albeit in a slightly different (but very similar) way. In the end, I uploaded to the arXiv first but we will be submitting to the same conference. One of the authors admitted in writing that they started working on the project after attending my talk. It feels unfair and like my idea has been taken and presented as someone else's, but is this plagiarism?
The whole purpose of conferences and talks is to disseminate ideas and knowledge. In some sense, if you had published on the topic and someone else picked up the ideas and used them in a different context, you would probably feel pleased to hear about it. You feel differently because you happened to not have written a publication on the topic, but that's not the other person's fault -- they did what the purpose of talks is: They learned from others and are using the knowledge.
I fail to see that that is wrong. How long would you like others to hold on with using the knowledge that you presented to them before they can use it themselves?
It is plagiarism if they present your ideas as their own. If they give you credit in some way then it isn't plagiarism, even if it isn't very courteous. Plagiarism is about the proper attribution of ideas. Citation is the way to avoid it. In this case, not enough is known here to make a real judgement, and, you say, they took them in a different direction.
Perhaps you have an opportunity, however, to work with them on these ideas jointly so that attribution is no longer an issue.
Note that you don't "own" ideas. Plagiarism isn't really about "stealing" what another "owns". It is a concept in scholarship that creators should be recognized.
Caveat: Laws vary and I've heard that some forms of plagiarism might be illegal in some places, but that isn't the norm.
The National Science Foundation Research Misconduct regulation defines plagiarism as the appropriation of another person’s ideas, processes, results or words without giving appropriate credit. I cite this source as one of many using the same formulation. Here it is clear it is also the idea that is the property of the "inventor", the persons intellectual property. And strictly based on that statement it seems like a clear case of property theft or plagiarism IF the source of the original idea is not given credit.
To take someones idea and develop it further is not in itself a problem, it is how science works. What is a problem is if the origin of an idea is not ones own and is not credited. Then it is intellectual property theft and something a reasearcher should avoid at all cost. What can be done in the individual case becomes a question of what one is willing to endure. An article based on the idea could be questioned by writing to the journal editor and explaining the case. In thge specific case where it seems two papers originating from the same idea will be published, it will depend on how "the other" paper presents the original idea and then something for the proceedings (equiv.) editor(s) to consider.
Plagiarism and intellectual property issues are issues of ethics.