Tandem Repeat Proteins (TRPs) are a class of proteins with repetitive amino acid sequences that have been studied extensively for over two decades. Different features at the level of sequence, structure, function and evolution have been attributed to them by various authors. And yet many of its salient features appear only when looking at specific subclasses of protein tandem repeats. Here, we attempt to rationalize the existing knowledge on Tandem Repeat Proteins (TRPs) by pointing out several dichotomies. The emerging picture is more nuanced than generally assumed and allows us to draw some boundaries of what is not a proper TRP. We conclude with an operational definition of a specific subset, which we have denominated STRPs (Structural Tandem Repeat Proteins), which separates a subclass of tandem repeats with distinctive features from several other less well-defined types of repeats. We believe that this definition will help researchers in the field to better characterize the biological meaning of this large yet largely understudied group of proteins.