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But it's both isn't it? Labour try and offer some stuff for those who are to the right of the members because that's where they're lacking support; however they don't try and change all of their policies, with the aim that when they're in power those same voters are convinced by the whole package and they get a further left policy platform than the Tories.
obviously when labour do it, they do so by reaching to the right, when Tories do it, they reach to the left...
By enacting righter policies to convince them, and trying to keep any lefties on board by keeping those policies as palatable as possible. Although I also think it does actual work the other way to some extent when Rishi steals a load of labour policies and sells them to the right, although still manages to cut Tory donors in.