Upgrade is the process of improving something by replacing part of it or adding additional parts, and it refers to the result of the process. For example, one can upgrade a computer by replacing the CPU with a faster one and by adding more RAM, and afterwards, the computer is an upgrade. Although often used in the context of technology, anything can be upgraded; improved.
Often an update is an upgrade but not always. Update only implies newer; more up-to-date. An update could degrade, or changing to an older version could be an upgrade.