All three are in the same family and are typically warm-season vegetables. As Rebecca pointed out, marrow has a striped appearance. Cucumbers are usually green and come in different lengths although some are white, yellow, or round.
Zucchini squash is also typically green, but some varieties are yellow or striped. Marrow is like a mature zucchini w/ a striped/speckled more leathery, ridged skin. It is usually cooked and is excellent for stuffing w/ seasoned meats and vegetable combinations. Zucchini can be eaten raw or cooked in many ways, and is a main ingredient in ratatouille, a French vegetable stew. Cucumbers are eaten raw in salads or cooked, ,pickled, and chilled as relishes and garnishes. I like them w/ garlic, rice vinegar, and plain yogurt as a zesty side to BBQ or Middle Eastern dishes.