verbs - Difference between "stick with" and "stick to"?

The more I think about it the more confused I get:

One good example is here:

Hmm. Maybe something like this. It's the end of the day and things
didn't go well. We're meeting to talk about what we'll do tomorrow.
Should we stick with the original plan or try something new?

We're at work, and I wander by to see how everyone is doing. You think
that you'd like to try something difference. "Stick to the plan for
now," I say.

So maybe while planning - stick with, and while doing - stick to?

I'm speculating ... sometimes the more you think about something the
harder it is to remember.

Is there a difference between

to stick with something/somebody

and

to stick to something/somebody

...and if so could you please give examples that make the different usages clear?

Answer

On the forum you linked to, a long catalog of uses was posted at 20-Mar-2008, 08:27. I think that posting makes clear that

1. there is no difference between the two phrases in the senses of "continuing to support/accompany/practise/adhere [figuratively] to": stick to/with the plan, stick to/with me, stick to/with your principles

ANOTHER EDIT: You may find one preposition used more often with any particular object stuck to—see bib's response—but this doesn't exclude using the other.

1. only stick to may be used to signify "cause to adhere to": stick the poster to the wall but not stick the poster with the wall.




2. only stick with may be used to signify "impose a (relative) burden upon": he stuck me with the bill or she got the fellowship, I was stuck with an assistantship, but to won't work in these.

One more "stick to" idiom occurs to me: *stick it to [someone]", meaning "inflict excessive (physical, emotional, financial &c) pain upon": They had him cornered and really stuck it to him.

EDIT: And another: Stick to [one's] guns, although it fits use 1 above, is a fixed idiom; stick with your guns would mean "continue to accompany your artillery".