Hawley retainers are the "traditional" retainer; here's a link to some images:
hawley retainer - Google Image Search
They have the wire across the front of the teeth which can be bent to move the teeth if they shift.
Essix retainers look like Invisalign trays;
essix retainer - Google Image Search
These can also be used to move teeth my putting "bumps" in the plastic.
Typically essix retainers have a limited shelf life - after 6 months or so they aren't as tight, become brittle or break. This doesn't happen in all cases, but it can. Hawley retainers are a little more sturdy if they are well taken care of.
Some orthos choose not to use bonded (permanent) retainers because it leads people to believe they don't have to wear their regular retainers, and that's not the case. The bonded retainer provides EXTRA retention, but alone does not provide ENOUGH retention to keep the teeth from shifting. Beyond that, they normally only go over the front four teeth, which means your other teeth aren't being retained at all (if you don't wear the removable ones) and are more likely to shift. A lot of orthos don't use bonded retainers, it seems to be a personal preference. Many, however, will apply one if the patient asks/insists.
Unfortunately he really has no legal obligation to fix the problem tooth, but it would be the ethical thing for him to do. I would venture to guess he will attempt to fix it because it ruins his reputation if he doesn't. You should talk to your ortho, however, because there may be a reason the tooth isn't where it is supposed to be; adults seldom receive "perfect" results. It could be your wear patterns don't allow the tooth to go into proper position, in which case shaving or IPR might be an option. Then again, sometimes wear is wear and it's too bad to "repair".