Background and Objectives: Amidst the COVID-19 pandemic, concerns about the psychological impact of disease-related anxiety on public health have risen. This study aims to compare general and death anxiety levels between acute coronary artery syndrome and COVID-19 pneumonia patients. Materials and Methods: A cross-sectional study of 132 individuals, including acute myocardial infarction (MI), COVID-19 pneumonia patients, and healthy volunteers from Trakya University Hospital (Turkey), was analyzed. Validated scales like the Beck Anxiety Inventory (BAI), Coronavirus Anxiety Scale Short Form, and Thorson-Powell Death Anxiety Scale (TPDAS) were employed. Demographic data such as age, gender, income levels, employment status, presence of a close relative with COVID-19, and whether participants followed COVID-19-related news were collected and compared across groups with significance level of 0.05 set for all analyses. Results: Among 41 COVID-19, 41 MI, and 50 healthy subjects, the pneumonia group showed highest COVID-19 anxiety (p = 0.01) and BAI scores (p = 0.008). Both COVID-19 and MI patients had significantly higher BAI and TPDAS scores compared to healthy controls (p < 0.001). Factors like female gender (p = 0.004), low education (p = 0.003), current employment (p = 0.008), and low income (p = 0.002) correlated with higher BAI scores. Low income (p = 0.001) and COVID-19 news exposure (p = 0.002) correlated with higher TPDAS scores. Males and married patients had lower anxiety scores (p = 0.008). High income, education, and employment reduced anxiety levels (p = 0.008). TPDAS scores decreased with higher income (p = 0.001), but increased in the MI group (p = 0.002) with COVID-19 news exposure. The multivariate linear regression analysis found that MI and COVID-19 pneumonia were associated with TPDAS; female gender, university education, and COVID-19 pneumonia with the Beck scale; and COVID-19 pneumonia with anxiety scores on the COVID-19 Anxiety scale. Conclusions: This research showcases differing anxiety patterns between illnesses such as MI and COVID-19 pneumonia amidst the pandemic, emphasizing the amplifying influence of media coverage on death-related anxieties. It underscores the imperative of targeted interventions and socioeconomic considerations in managing psychological consequences and formulating responsive public health strategies.