You are right in assuming they are different, but your opinion that a terminated project does not necessary mean that it failed is not accurate. A terminated project is a project that is doomed to fail, but pulling the plug on the project happened prior to its actual failure.
The difference between project termination and project failure is that the former is proactive and the latter is reactive. This means that in case of a project termination, the project stakeholders/project manager, after assessing a project, decided to terminate it, and allocate the resources/funds elsewhere. The project failed, as it was not successful (a project can only have 2 states, successful or failed).
When it comes to project failure, this means that the project was allowed to continue beyond the point where it should've been terminated. The project failed, but in this case it cost more money and hours than it should have, had the stakeholders and the project manager killed it (terminated it) when they saw the first warning signs.