Demonstrate is you'll make clear by reasoning,something with an action to make things clear.While show means you'll permit the other person to see something without any clear action of what is it.

First take a look at the meanings : ***************************************************************************************** DEMONSTRATE is a verb which means : 1. to make evident or establish by arguments or reasoning; prove: to demonstrate a philosophical principle. 2. to describe, explain, or illustrate by examples, specimens, experiments, or the like: to demonstrate the force of gravity by dropping an object. 3. to manifest or exhibit; show: He demonstrated his courage by his actions in battle. 4. to display openly or publicly, as feelings: to demonstrate one's anger by slamming a door. 5. to exhibit the operation or use of (a device, process, product, or the like), usually to a purchaser or prospect: to demonstrate an automobile. ***************************************************************************************** SHOW is a verb too and has many shades of meanings. But when used with an object just the way demonstrate is used, it means the following : 1. to cause or allow to be seen; exhibit; display. 2. to present or perform as a public entertainment or spectacle: to show a movie. 3. to indicate; point out: to show the way. 4. to guide, escort, or usher: He showed me to my room. Show her in. 5. to explain or make clear; make known: He showed what he meant. ***************************************************************************************** Now compare the meanings. Except in the 5th meaning of show, it can not be replaced with demonstrate in any other. Similarly except the 3rd and 4th meaning of demonstrate, nowhere can it be replaced by Show. In general the difference between them is that demonstrate is to show / prove / explain / display publicly usually with the help of examples, show means to exhibit / point out / escort / explain or perform :) the examples given above will help you to differentiate between the two better :)