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At first I was under the impression that latent variable models and graphical models were different things altogether, but after reading some papers about the former class of models, it seems they have more in common than I thought. For instance, in both cases there's a specification of the conditional probabilies. Is there any distinction between the two? How can I view these in relation to each other?

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I would go for a reference book on machine learning and graphical models. For example,

Machine Learning: A Probabilistic Perspective

Pattern Recognition and Machine Learning

As for your question, latent variable models are graphical models where some variables are not seen, but are the causes to the observations. Some of the earliest models were factor analysis. Here the idea is to find a representation of data which releveals some inherent structure of the data. You may want to have a look at the publications by Christopher Bishop (the author of the second book) on the topic.

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