These two tests are the source of all confusions. Are they siblings? Independent? One started earlier, then an internal war caused the co-founder to establish another (but carefully designed to be similar) brand? Most importantly, WHICH MATTERS?
Last week I took the TOEFL test and finally got it:

TOEFL is for getting into (presumably) American university.
TOEIC is for getting a job, especially in Asia.

TOEFL is expensive – USD$150.
TOEIC costs less – USD $55 or so. Lesser of the two evils.

TOEFL is strictly (American) English.
TOEIC is partially localized (the instruction part). Still, American English.

TOEFL is difficult to cheat. They put you in a cubicle. Also, the photo ID check is rigorous.
TOEIC is easier to cheat. 100 test takers in a huge classroom in a university, allowed to bring in their own bags – sounds too familiar.

TOEFL takes three hours. During the last hour, the most difficult thing is the internal battle – to suppress the rage coming from exhaustion and focus on the test itself.
TOEIC takes two hours. Enough said.

TOEFL forces you to speak and write.
TOEIC spoils you – only reading and listening. No wonder it is so popular in Asia.

But after taking both tests, my impression is –
TOEFL score might represent an accurate communication skill.
TOEIC score says nothing – taking 800 out of 1000 might let someone join the "skilled" labor market, but my experience tells me that 900 is barely enough to guarantee "real" skill – like taking a cab or asking for a cup of coffee. We can blame the lack of speaking test, and the whole industry based on tricking students into getting high TOEIC score.
I never used those "trainings" but I did use the TOEIC illusion in the past – snatching a job without prior experience because of the higher score.