Mostly you would use an url alias for your page. Automatically it sets the tilte as alias. If you change the title, the alias changes too and the old url alias might no longer work.
For this it's useful to know the static link to your page!You can get the static link if you hover over the edit button and look at the bottom left in most browsers. It should look like "node/123". The number is the node id, which is unique to every page and will never change.