I have an analogy for (ASL) interpreting from a Deaf user's perspective that involves parachutes and squirrel suits and such. Ian Smith asked for it to be publicly available, so... here is a hastily written post. Perhaps someday it will be edited into something more eloquent; today is not that day.
Ok. So you know wingsuits (sometimes called squirrel suits after the flying squirrels they resemble), the skydiving suits with wings that let you kinda glide around? (If you don't, here's a video of one.)
That’s lipreading. It looks like flying, but really it’s more like... "falling, with style," to quote Toy Story. To the untrained eye, squirrel suiting can masquerade as flying, but you can’t actually continue doing it. You have to bail out of it and activate your parachute at some point before you smash your head open on a rock.
Interpreters are like the giant flying eagles from the end of the Lord of the Rings. (And yes, that's what it looks like on the inside after lipreading, sometimes. Not all the time, but... sometimes.)
Giant eagles can swoop in and pick you up -- and when they do, you are obviously definitely not flying on your own. It's all a bit, uh... bulky and noticeable, but also, you're... not smashing your head open on a rock. And you can keep flying for a lot longer.
I haven't really thought through the parallel analogy for captioning, but perhaps it's like steering your fall over one of those giant fans like they have for indoor skydiving places. It shoots you upwards, it can work for "flyers" (hearing people) as well, but the captioning isn't portable - it only shoots air upwards from that one spot.
Anyway. I explain this to my interpreters at conferences and such (it's really fun to explain using ASL classifiers), and will also tell them that sometimes I will jump off their backs (so to speak) and squirrel-suit for a bit. It's not a reflection on their skill (they can be the best interpreter in the world, and I'll still do it!) or my need for the access they provide -- it's because that’s how I use all my tools/options with fluency.
I can get to some places with my squirrel suit that they can’t quite reach as giant eagles. When it's working, it works beautifully -- I’ll jump on and off really fast, and the choreography of a good interpreter/Mel team can be gorgeous when it works out.
Just for fun:
The Star Wars Ep II scene of Anakin jumping out of the shuttle is actually a fairly accurate portrayal of extroverted puppymel asking questions of a... somewhat less extroverted person, with the requisite ADHD losing-of-things.
And a conversation that happened amongst Deaf friends when I was explaining the analogy:
Samir: Why couldn't my terps have swooped in to pick me up to take me to Mordor in the first place?
Mel: One does not simply walk into Mordor.
Mel: One requests reasonable accommodations, then works one’s way through an increasingly bureaucratic chain, then says “sod it” and walks into Mordor, because it’s easier that way sometimes.