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¿Hay alguna diferencia entre usar INT(1) y TINYINT(1) en MySQL?

¡Aquí lo entenderás mejor!

tinyint: 1 byte, -128 to +127 / 0 to 255 (unsigned)
smallint: 2 bytes, -32,768 to +32,767 / 0 to 65,535 (unsigned)
mediumint: 3 bytes, -8,388,608 to 8,388,607 / 0 to 16,777,215 (unsigned)
int/integer: 4 bytes, -2,147,483,648 to +2,147,483,647 / 0 to 4,294,967,295 (unsigned)
bigint: 8 bytes, -9,223,372,036,854,775,808 to 9,223,372,036,854,775,807 / 0 to 18,446,744,073,709,551,615 (unsigned)