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The headline for the second article is with regards to prioritizing vaccination in places where demand outstrips supply. The conclusion of the study is:

"Individuals who have had SARS-CoV-2 infection are unlikely to benefit from COVID-19 vaccination, and vaccines can be safely prioritized to those who have not been infected before."

And from the body of the article:

"Experts say that more research is needed to determine how long immunity lasts after a case of COVID-19. Until we have that data, some infectious disease specialists are recommending that people who’ve had COVID-19 still get one dose."

And:

"Given the limited availability of the vaccines in certain countries, the findings add to the growing belief that the vaccines should be prioritized for those who haven’t previously had COVID-19."