They're not at all fully interchangeable, just many Americans have a poor grasp of the English language.
They're not at all fully interchangeable, just many Americans have a poor grasp of the English language.
I would wager that for the majority English speakers, the words "theft", "robbery", and (to a lesser degree) "burglary" or more or less fully interchangeable.
They may not be interchangeable in law, but the usage of English in law is famously not always in line with common usage, which is why we have "legalese" which many completely fluent and native English speakers may have trouble understanding without specialized legal training.
If you'd like it packaged in something that looks authoritative, you might consider the following definitions from Merriam-Webster:
burgle: to commit robbery
rob: to take away as loot : steal
thieve: steal, rob
But the law is using the language incorrectly in ways that are guaranteed to cause confusion. This is a problem. The law should be using the language correctly, which it isn't doing now.
The law does not require nor permit you to bring your own dictionary for crimes; they give you the definition for free and require to use theirs. As an example, burglary is defined in
Texas Penal Code § 30.02 - Burglary: https://tcss.legis.texas.gov/resources/PE/htm/PE.30.htm
They further go on to define "building" and "habitation" in Penal Code § 30.01.
If you find a dictionary definition that conflicts with the Texas Penal Code's definition of burglary or of a building, guess which one prevails in a criminal proceeding in Texas?
For example, imagine that someone gets really drunk, stumbles into your home, collapses on your couch, and soaks it in urine. Hours later, you come home and find him sleeping it off.
Under Texas law, whether this is "burglary" depends on the value of your couch.
Suppose you've got a very fancy couch. It was "burglary". Any local newspaper is free to refer to that guy as having been convicted of burglary (assuming he gets prosecuted). But this is clearly a miscarriage of justice; no one in the world would consider that "burglary", and coverage using that term should be defamatory.
In general, if you seek to define new terms, they should actually be new terms. Redefining terms people already know has downsides, but not upsides.