I can ensure you that nothing will happen to your dog. I am going to insure my car so if something happens to it, I wont have to pay for damages.

the two words can be exchanged in most situations,but when it comes to insurance,you can only use insure.personal opinion.

İnsure is to buy insurance for(something,such as property, or to make (something) süre certain Or safe Ensure is make certain that(something) will occur or be the case, To make secure or safe, as from harm.