I need help understanding the difference between apud and ĉe

Lernu defines

apud (apud· ← apud)
next to, beside

ĉe
at, beside, with

I guess my problem is learning it from the English word "beside"

another definition of ĉe is
at, near, beside, with (memrise.com)

but when you search "near" in lernu you get
proksime, proksima, proksime de, proksime al; apud, preskaŭa

notice apud, not ĉe

so is "near" in the definition of ĉe?
and what the hell of 'beside'?

I am near a trainwreck
I am beside a trainwreck
I am next to a trainwreck
I am with a person about to be a trainwreck

Thank you so much for all of your help, I swear I will be competent in this lingvo,
See you at NASK!

Proksima contrasts with fora or malproksima.

Mi loĝas tre proksime al la stacidomo - I live close to the railway station.

Apud has the idea of next to - sidiĝu apud mi - come and sit next to me.

Mi renkontos vin ĉe la restoracio - I'll meet you at the restaurant.