The differences between cloze-task language model (LM) probing with 1) expert-made templates and 2) naturally-occurring text have often been overlooked. Here, we evaluate 16 different LMs on 10 probing English datasets -- 4 template-based and 6 template-free -- in general and biomedical domains to answer the following research questions: (RQ1) Do model rankings differ between the two approaches? (RQ2) Do models' absolute scores differ between the two approaches? (RQ3) Do the answers to RQ1 and RQ2 differ between general and domain-specific models? Our findings are: 1) Template-free and template-based approaches often rank models differently, except for the top domain-specific models. 2) Scores decrease by up to 42% Acc@1 when comparing parallel template-free and template-based prompts. 3) Perplexity is negatively correlated with accuracy in the template-free approach, but, counter-intuitively, they are positively correlated for template-based probing. 4) Models tend to predict the same answers frequently across prompts for template-based probing, which is less common when employing template-free techniques.