All answers are correct from my point of view, but missing one major use case for "between page". It is used mainly (and should be used) where users can input their own data/links etc. that are visible to others. The reason is to warn users they are leaving so there is no security risk.
Take Steam for example. Users can add links to their reviews and those links can lead to external web that can be designed as steam site. Without warning, users might think they are still on steam and input passwords, names, cc, etc. The inconvenience coming with extra step is overcame by security.
So to sum it up - It's standard practice to have different link in and out of your app/site (icon/different style); you should use inter step only if it can be security risk or you absolutely have to let the user know he's leaving.