Can a positive change result in positive stress? I have been researching the differences between stress and anxiety to understand them for my own curiosity. My basic understanding is that stress is a variation from routine or something that upsets your normal balance while anxiety is worry about something when there is no stressor.

My question, then, is this: if stress is caused by change to normal routine, would a good change with only positive effects still be considered stress? For example, going on vacation. The travel could certainly be stressful (or perhaps just anxious), but once a person arrives, lets assume they have a very good, relaxing stay. Could this be considered a stress since it is a change from the normal routine, despite having no negative effects?

I admit that most likely the answer lies in a misunderstanding I have about the definition of stress, but I am curious...
It sounds like you're looking for the word "eustress" or "good stress". Which isn't exactly a label of stress, which as commented is negative, but a positive perception of stress. 

My favorite go to example is the positivity often associated with, "challenge accepted!" Here we have a change that is often motivational, difficult, and identifiable as worthwhile.