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.