Haemorrhoids ussually cause bright red blood that you will mostly see on the toilet paper. A simmilar cause is an anal fissure which is a crack or tear in the anal canal. It is incredibly painful.
Diverticular disease is also another very common cause of blood in the stool. Diverticular disease is where pockets form in the wall of the bowel and as you become older it is more likely that you will develop them. The blood may be bright red or darker red but will be plainly identifiable as blood.
Inflammatory bowel diseases such as Crohn’s or ulcerative colitis can also cause blood in the stool but is most often combined with very watery diarrhea multiple times a day.
Colorectal polyps (small growths in the bowel wall that may turn into cancer) can also cause blood in the stool although it would probably be in such small quantities that you would not see it with naked eye (hence the occult feacal blood test you took
People who have liver disease sometimes develop rectal varices that can bleed profusely although the most common place for varices to devolop would be the oesophagus and stomach.
As others have said ibuprofen, aspirin and other NSAID’s can cause damage to the lining of the stomach and the duodenum. While the extreme would be an ulcer there is a whole range of things it can cause including gastris and small errosions (ie not big enough to be an ucler yet). Alcohol can also cause gastritis.