As Large Language Models (LLMs) are integrated with human daily applications rapidly, many societal and ethical concerns are raised regarding the behavior of LLMs. One of the ways to comprehend LLMs' behavior is to analyze their personalities. Many recent studies quantify LLMs' personalities using self-assessment tests that are created for humans. Yet many critiques question the applicability and reliability of these self-assessment tests when applied to LLMs. In this paper, we investigate LLM personalities using an alternate personality measurement method, which we refer to as the external evaluation method, where instead of prompting LLMs with multiple-choice questions in the Likert scale, we evaluate LLMs' personalities by analyzing their responses toward open-ended situational questions using an external machine learning model. We first fine-tuned a Llama2-7B model as the MBTI personality predictor that outperforms the state-of-the-art models as the tool to analyze LLMs' responses. Then, we prompt the LLMs with situational questions and ask them to generate Twitter posts and comments, respectively, in order to assess their personalities when playing two different roles. Using the external personality evaluation method, we identify that the obtained personality types for LLMs are significantly different when generating posts versus comments, whereas humans show a consistent personality profile in these two different situations. This shows that LLMs can exhibit different personalities based on different scenarios, thus highlighting a fundamental difference between personality in LLMs and humans. With our work, we call for a re-evaluation of personality definition and measurement in LLMs.