>I feel like it's a mistake for the legal code to distinguish between what are fully interchangeable terms in the language the code is supposedly written in.
They're not at all fully interchangeable, just many Americans have a poor grasp of the English language.
The language is solely defined by what people think it means. The terms are in fact fully interchangeable.
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