The dividing line
Adjustment of status happens inside the United States. Consular processing happens at a US embassy or consulate abroad. Eligibility to adjust generally depends on having been inspected and admitted or paroled, on your status history, and on whether a bar applies to you. Some people have a choice. Many do not.
Why leaving can be the risk
For someone who accrued unlawful presence, departing to attend a consular interview can trigger a bar on returning. That is the scenario the provisional waiver process exists to address, by resolving the issue before departure rather than after. Nobody should book travel for an interview without knowing whether this applies to them.
What each route gives you
Adjustment usually allows a request for work and travel authorisation while the case is pending, and it keeps you in the country. Consular processing can be faster in some categories and is the only option for many people abroad. Interview practices differ between the two.
Decide before you file
This is the single assessment most worth getting right at the start. A filing made on the wrong assumption is expensive to unwind and can affect eligibility later.
