Local surrogate approaches for explaining machine learning model predictions\nhave appealing properties, such as being model-agnostic and flexible in their\nmodelling. Several methods exist that fit this description and share this goal.\nHowever, despite their shared overall procedure, they set out different\nobjectives, extract different information from the black-box, and consequently\nproduce diverse explanations, that are -- in general -- incomparable. In this\nwork we review the similarities and differences amongst multiple methods, with\na particular focus on what information they extract from the model, as this has\nlarge impact on the output: the explanation. We discuss the implications of the\nlack of agreement, and clarity, amongst the methods' objectives on the research\nand practice of explainability.\n