What is the primary distinction in the appropriate usage between the grammatical markers '-는 셈이다' and '-는 모양이다' when expressing an inference?

The primary distinction lies in the level of certainty and the basis of the inference. '-는 셈이다' expresses a logical conclusion or a strong inference based on clear, objective evidence or calculation; it implies a high degree of certainty that something is the case. For example, '세 시에 출발했으니까 지금쯤 도착하는 셈이다' (Since we left at three o'clock, we should be arriving about now) implies a calculated estimation. Conversely, '-는 모양이다' expresses an inference based on observation or outward appearance; it indicates a weaker, more tentative conclusion based on subjective impressions or indirect evidence. It suggests the speaker is making an educated guess rather than stating a fact. For example, '밖에 비가 오는 모양이다' (It seems like it's raining outside) suggests the speaker is inferring rain based on seeing wet streets or hearing sounds suggestive of rain, but without direct confirmation. Therefore, '-는 셈이다' communicates a reasoned judgment with considerable confidence, whereas '-는 모양이다' conveys a more cautious assessment based on observable cues.