[R] AIC() vs. mle.aic() vs. step()?

[Alexandra Thorn]

I know this a newbie question, but I've only just started using AIC for
model comparison and after a bunch of different keyword searches I've
failed to find a page laying out what the differences are between the
AIC scores assigned by AIC() and mle.aic() using default settings.  

I started by using mle.aic() to find the best submodels, but then I
wanted to also be able to make comparisons with a couple of submodels
that were nowhere near the top, so I started calculating AIC values
using AIC().  What I found was that not only the scores, but also the
ranking of the models was different.  I'm not sure if this has to do
with the fact that mle.aic() scores are based on the full model, or some
sort of difference in penalties, or something else.

Could anybody enlighten me as to the differences between these
functions, or how I can use the same scoring system to find the best
models and also compare to far inferior models?

Failing that, could someone point me to an appropriate resource that
might help me understand?

Thanks in advance,
Alexandra