The novelty of the coronavirus disease 2019 (COVID-19) pandemic is that it is occurring in a globalized society enhanced by digital capabilities. Our aim was to analyze the psychological and emotional states of participants in different pandemic-related contexts, with a focus on their digital and physical distancing behaviors. The online survey was applied during the ascending phase of the pandemic in March 2020 in two neighboring EU countries: Italy and Croatia. The study subjects involved four groups, two directly affected by epidemiological measures and two serving as controls—(1) participants from Italy who were in lockdown (Italy group), (2) participants from Croatia who were not in lockdown but who were in direct contact with an infected person and underwent epidemiological measures (CRO-contact group), (3) participants from Croatia who were in an analogous situation but not near the same infected person (CRO-no contact group), and (4) participants from Croatia who were not aware of any infected person (CRO-unrelated group). The survey consisted of validated scales of psychological and emotional states, and custom-made questionnaires on the digital (online) and physical (off-line) behavior of the participants. The Italy group in lockdown had higher self-perceived scores for depression, stress, post-traumatic intrusion, and avoidance, as well as the highest digital activity and physical distancing than the not-in-lockdown Croatian groups. The insight into the extent of online activities and off-line isolation allowed for the introduction of Digital Activity and Physical Distancing Scores. Self-perceived post-traumatic avoidance was higher in both the Italy and CRO-contact groups than the control CRO-no contact and CRO-unrelated groups, and higher avoidance correlated with higher Digital Activity and Physical Distancing Scores. Being in direct contact with the infected person, the CRO-contact group had no other alterations than unexpectedly lower post-traumatic hyperarousal when compared with the Italy group. The Italy group in lockdown demonstrated higher self-perceived psychological toll together with higher digital activity and physical distancing than Croatian groups not in lockdown, even when compared with the affected CRO-contact group. The study outcomes suggest that the general emergency measures influenced citizens in lockdown more than exposure to the virus through direct contact with an infected person.