Hosting gives your website a place to run. Maintenance is the recurring work that keeps the website healthy after it is running.
Hosting typically covers infrastructure resources, networking and the environment in which the website operates. The exact responsibilities vary by provider.
Maintenance can include software updates, security checks, backups, performance work, content changes, monitoring and technical support.
For a business-critical website, define both layers clearly so there is no confusion about who responds when a website is unavailable or an integration breaks.