I can't figure out how self-hosted and "deploy on cloud" are not mutually exclusive. Unless you've gone through the trouble of setting up enough machines at home to have a viable cloud infrastructure.
"Deploy to cloud" is just an answer to the "where and how" - a singular option.
This is (typically, though not always) different from SaaS and on-prem, the former being hosted/managed/monitored by a third party, and the latter meaning hosted by you, usually managed and monitored by a third party - often for regulatory or whitelabelling reasons.