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When a problem says: Grace helps move the sofa if but only if Heather helps move the recliner, do I diagram it as: Gs(------)Hr or Hr(----)Gs, or does it matter either way? Also are "if BUT only if" and "if AND only if" diagrammed differently or the same?
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You can diagram it either way. Think of a biconditional like this: The variables included are both sufficient and necessary conditions. Since you're drawing two arrows, it doesn't matter which variable goes on which end.
Typically on the LSAT, "and" = "but" and vice versa. This is often true in regard to conditional logic.
For instance, "I'll go to the store and i'll pick up Jim from school" is equivalent in meaning to "I'll go to the store, but i'll pick up Jim from school"
does it matter either way?
Nope, both are equivalent.
Also are "if BUT only if" and "if AND only if" diagrammed differently or the same?
The same.