Bad guys don't like these words because they often describe jail terms: concurrent means "at the same time," and consecutive means "one after the other in a series." Con artists would rather serve concurrent terms and get them over with, instead of consecutive ones.
Concurrent events happen at the same time, like when thieves make a plan to rob two houses at midnight. Here are some examples — don't try to read them all at once:
Most patients ultimately require at least two concurrent treatments to achieve remission of their depression, he said. (New York Times)
A second Esquire promotion, meanwhile, is concurrent with its Brooklyn Decker effort, with both running through Feb. 28. (New York Times)
He was given 20 concurrent life sentences, and has been held for nearly 30 years in the Broadmoor high-security psychiatric hospital west of London. (New York Times)
The adjective consecutive, on the other hand, means "one after the other," like little ducks all in a row. Thieves go from one house to the next on down the block if they're robbing consecutive houses. Sports fans like the word consecutive, especially when their team is winning. Here are some consecutive examples, read them one at a time:
Harvard also won its 19th consecutive game at home. (Seattle Times)
Each team will have to play on three consecutive nights at least once. (Seattle Times)
South Korea's factory activity shrank for a fourth consecutive month. (Reuters)
If the robbers served time consecutively, they'd serve first two months for robbing houses, and then another two months for stealing a car. If they served time concurrently, they'd be out in just two months.