1- A table for two people please. 2- A table for two persons please. Generally, persons is a decent substitute for individuals, and appears more in legal contexts that demand precision. People is the ordinary plural of person. Asking for a table for two or a table for two people is better than asking for a table for two persons.

Both are correct, but you would see them in different contexts. You would only see 'two persons' in formal written contexts, such as official documents and technical/legalistic notices. For example, there is always an official sign in lifts/elevators saying, for example, 'Maximum capacity eight persons.' This is a legal requirement, so the formal term is used. In all other situations, including all spoken contexts, we use the plural 'people'. Unless you are a lawyer, you will probably never need to use the word 'persons'. You can forget about it.

hope this helps The noun person has two plurals: persons and people. Most people don’t use persons, but the sticklers say there are times when we should. “When we say persons,” says Wilson Follett’s Modern American Usage, “we are thinking, or ought to be, of ones—individuals with identities; whereas when we say people we should mean a large group, an indefinite and anonymous mass.” The traditional rule is that persons is used for either an exact or a small number. So we might estimate that a hundred people were there. Or if we know the exact number, we’d say ninety-eight persons were there. As for “a small number,” how small is “small”? In Words on Words, John B. Bremner suggests fewer than fifty. Theodore M. Bernstein concurs, saying in The Careful Writer that fifty people is acceptable. To Bernstein, two people is nearly unthinkable but 4,381 persons is “quite proper.” Meanwhile, the language moves on. In A Dictionary of Modern American Usage, Bryan A. Garner calls the persons-people distinction “pedantic.” Garner says that twelve persons on the jury “sounds stuffy” and that most Americans today would say people instead. Roy H. Copperud agrees. In A Dictionary of Usage and Style he dismisses the grammatical superiority of persons as “superstition,” a law that “usage has in fact repealed.” Because persons sounds aloof and clinical, the word still thrives in legal, official, or formal usage. A hotel chain’s website offers “options for three and more persons.” Elevators carry signs saying, “Occupancy by more than eight persons is unlawful.” The Department of Justice has a database called the National Missing and Unidentified Persons System.