Two architectures
A cloud time-attendance platform keeps the software and the data on the provider's servers, and the company accesses it through a browser or an app. Running your own server means the same kind of software (ZKTime, for instance, paired with ZKTeco terminals at the door) installed on a machine inside the building, which the company maintains itself.
Cost and upkeep
A cloud setup needs no server purchase and no IT staff to maintain it — updates, security patches and uptime are part of the service, paid through a subscription. Your own server needs an upfront hardware investment and someone's regular time (in-house or an outside IT contractor) to keep it running, but after that investment there's no monthly subscription for the software itself.
Control over the data
Your own server keeps time-attendance data physically on site, under the company's direct control — important wherever internal policy or a client contract explicitly requires that. A cloud platform asks you to trust how the provider handles that data; the standard that handling gets measured against is ISO 27001, a certification for managing information security.
Backup and continuity
On a cloud platform, redundancy and backup are typically built into the service — the provider handles them as a standard part of the subscription. On your own server, backup is the company's responsibility: without a specific plan, a single failed drive can mean months of attendance records lost with no way to recover them.
Recommendation
For a company without in-house IT staff, a cloud platform (like one that has run since 2010, on ZKTime software over ZKTeco terminals) removes the maintenance and backup burden from the company and is usually cheaper in the short run. For an institution with a strict internal policy on keeping data within its own infrastructure, running your own server remains a reasonable choice, with a clearly assigned owner for backup. Terminal, card and integration detail lives on the time-attendance page.