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Shoplifting relates more to the physical possession of goods.
A shoplifter may pretend to be a customer or buy some and steal many (or vice-versa). But while at a restaurant such pretense won't work. Stealing food too is different.
I came across a french word- Mouche- meaning 'fly' ...but could not find a proper ONE WORD substitute.
This is known as a Dine and Dash
A dine and dash (also referred to as "dine and ditch", "eat and run", "chew and screw" "doing a runner" or "beating the check") is a form of theft by fraud, in which a patron orders and consumes food from a restaurant or similar establishment with no intent to pay, then leaves without paying. Wikipedia
A common phrase for that type of thing (at least in some areas),
is "runner", "a runner", "did a runner".
There is no difference between stealing food and eating food and not paying for it. The second is a subset of the first.
There are definitely terms for the act of eating at a restaurant and leaving without paying—chew and screw, dine and dash, or eat and run, for example—but I can't think of any that specifically refer to the perpetrator.
Mooch is a good start, but does not imply the illegality (since typically a mooch asks for what they don't pay for). Perhaps freeloader, parasite, or sponge, but again none of those have the implication of theft. Con artist captures the "trick" aspect of the theft, but has connotations of a hustler who convinces their victim to do something they would not ordinarily do (and waiters are always serving food).
So moving on to words describing theft: filcher might work and swindler seems apt, but neither is specific to this act.
This might be the time to make up a term: perhaps pie-jacker or sandwichbagger? ;)
I have heard the term "check walking" or "check walker" The idea being, they walk out without paying the check.
Slightly obscure, but you can use bilking (Oxford Dictionaries) - withholding money unfairly. This has been fairly frequently applied to people failing to pay at resturants, e.g. "Man who bilked El Bulli is found".
As Richard says in his comment there is also the term from the British Theft Act, making off without payment.
In the US I've heard this referred to as "choke-n-bolt".
The closest single word (as opposed to phrase) that I know is scarper, although scarper may also used be generally for any hasty exit to avoid consequences.
'dodger'--someone who resorts to dishonest tricks to avoid something unpleasant (like paying the check at a restaurant or leaving the gas station without paying after a fill-up). The Los Angeles Dodgers baseball team used to be called the Brooklyn (NYC) Dodgers, named after the 'trolley dodger'--someone who rides on the trolley and gets off without paying.
Bilking used to be a famous word in our university campus for eat and sneak types.
Stiffed as a transitive verb is to cheat someone out of money owed or not to pay someone an amount due or expected. “He stiffed me on the tip.” Encarta Dictionary North American
The legal term is "Defrauding an Innkeeper".
