From the Methods section of the Patone paper (your first link): "A self-controlled case series study of people ages 13 years or older vaccinated for COVID-19 in

From the Methods section of the Patone paper (your first link): "A self-controlled case series study of people ages 13 years or older vaccinated for COVID-19 in England between December 1, 2020, and December 15, 2021 [...]" In other words, all of the participants received covid vaccines. The second paper you've linked studied unvaccinated persons (mRNA-vax recipients were specifically excluded) and its claim of higher rates of myocarditis for covid infection is based other researchers' values of myocarditis incidence post-vax and, as alluded to in the Discussion section, skewed by relatively low 2nd-shot uptake among the American participants (myocarditis risk associated with mRNA shots goes up with each successive dose). The Israeli paper looks at myocarditis in persons before the vaccines became available (March 2020) and then afterwards. In Israel, 2nd shot and further shot uptake was much higher than in many other places.