Difference between dysentery and bloody diarrhea
Diarrhoea
Diarrhea is loosely defined as passage of abnormally liquid or unformed stools at an increased frequency. For adults on a typical Western diet, stool weight &gt;200 g/d can generally be considered diarrheal. Diarrhea may be further defined as  acute  if &lt;2 weeks,  persistent  if 2–4 weeks, and  chronic  if &gt;4 weeks in duration.
~Harrison's principles of internal medicine, 20$^{th}$ edition, page 261.


Dysentry
Dysentery is bloody diarrhoea, i.e. any diarrhoeal episode in which the loose or watery stools contain visible red blood. Dysentery is most often caused by Shigella species (bacillary dysentery) or Entamoeba histolytica (amoebic dysentery).
~WHO definition

One can also follow WHO definition of diarrhea for practical purposes but still I mentioned it from Harrison as it is more specific and quantified.
'Blood in stools' generally describe visible blood in stool, and the quantity of stool passed here can be normal like in upper GI bleeding if compared to diarrhoea or dysentry.
Diarrhoea can be classified into four major categories: Secretory, Osmotic, Malabsorbtive, and Exudative, in which exudative diarrhoea show such features of bloody stool.(~ Robbins basic pathology 9$^{th}$ edition page 577).
In fact, it is also clearly mentioned in Harrison in the topic of diarrhoea that:-

Invasive bacteria and  Entamoeba histolytica  often cause bloody diarrhea (referred to as  dysentery).

Conclusively, bloody diarrhoea and dysentry are the same.