The difference is the lacing. On an oxford, the quarters are sewn under the vamp — closed lacing, a tidy V. On a derby, the quarters sit on top — open lacing that spreads when you loosen the shoe.
Oxfords read more formal. Derbies are the everyday British-inspired leather shoe: easier on a high instep, quicker to put on, slightly more casual with jeans. YoyooBlue cuts both as leisure shoes, not court shoes.
Shop oxfords and derbies, or start with what derby shoes are.