Both platforms in Tableau are used to store visualisations, data sources and workflows however there are some key differences. Below you will find a summary of the points of difference.
Location
Tableau server is located at an organisation-specified location, therefore this is installed and maintained at the responsibility of the organisation. This differs from Tableau Cloud which holds the responsibility to host on behalf of the organisations that pay a subscription.
Cost
On a license-per-license basis, the costs can be minimally different. However, as the needs of a business grow, one may be preferential over the other. For the Tableau server, the right machinery and maintenance of the hardware are required. This means an upfront cost in addition to maintenance costs which the organisation will be responsible for. In contrast, Tableau Cloud is a subscription-based pricing model, therefore Tableau is responsible for hosting machinery and maintenance of this infrastructure for the cloud which would absorb these costs.
Accessibility
As Tableau Server is hosted within the organisation, running on their network, this can add ease of control to handle updates and back-up. For a more hassle-free option, Tableau Cloud will take responsibility for administrative tasks.