Bright red "live" blood can come from any part of the lower intestines. Strong-smelling feces with dark blood are called melena and are associated with bleeding in the upper gastrointestinal tract, peptic ulcers are a common cause. The reason for the difference is the blood gets digested as it passes through the gastrointestinal tract. It's not a 100% exact science, bleeding in the lower intestines might still spend enough time in the body to be digested and bleeding in the upper gastrointestinal tract might come out fast enough that it still looks red.

> fecal occult blood test

Often used to screen patients for colonoscopies. Screening is looking for disease in the asymptomatic: "occult" means it's not visible to the naked eye, you're looking for blood even though the patient has not noticed any. The symptomatic don't need screening, they need diagnosis and thus proceed directly to colonoscopy. Or endoscopy if upper gastrointestinal tract bleeding is suspected.