【Belch】 , 【burp】 , 【vomit】 , 【disgorge】 , 【regurgitate】 , spew,  【throw up】 are comparable when they mean to eject matter (as food or gas) from the stomach by way of the mouth or, in extended use, from a containing cavity by way of an opening.

【Belch】 denotes the noisy voiding of gas from the stomach and may be extended to something ejected in volume and often with noise (as smoke and fire from a cannon or a volcano).

【Burp】 in its basic sense in interchangeable with 【belch】 , but in extended use is much less forceful and usually refers to something sounding like a human 【belch】 .

【Vomit】 is the usual word for the ejection through the mouth of what has been eaten or swallowed; ordinarily it implies nausea, but it may suggest a previous gorging or surfeiting or the use of an emetic.

It is often used to suggest a forcible rejection or an emission or a discharge of contents.

【Disgorge】 , though close to  【vomit】 , more specifically implies an ejection of something swallowed, in essentially its original state.

Especially in extended use it may suggest an ejection or yielding up (as of something held or secreted) that is induced by force or pressure from without.

Basically 【regurgitate】 implies a flowing or gushing back, typically of food from the stomach to the esophagus or mouth.

In extended use 【regurgitate】 may reflect quite neutrally its basic

meaning, but more often it carries some suggestion of the unpleasantness of the physiological phenomenon.

Spew is rare in modern usage as a synonym for 【vomit】  but has extended use as connoting a pouring forth in a stream that cannot be restrained or, sometimes, a spurting or spitting forth.

It also may imply specifically a pouring forth of something offensive (as abusive or foul language).

Basically 【throw up】 is closely equivalent to 【vomit】 , though it may stress the matter ejected rather than the physiological process.

In extended use it is distinctly less vigorous than 【vomit】  and usually implies no more than a producing or bringing forth of something.