1. What cloud is
Terminals send data to a base maintained by the provider. You use the software and do not worry about the server. A separate base per client, a daily data copy, pay by use.
2. What your own server is
Licences are installed on your server. You maintain the system and base. It makes sense when internal rules forbid outside hosting or when you want full control.
3. Upkeep
Cloud is maintained by the provider. Your own server is maintained by you — or someone you pay. If you have no IT, cloud is simpler.
4. Data and copies
With cloud, a copy is made daily. With your own server, copies are your responsibility. The base can be transferred with your own server — an advantage when you change infrastructure.
5. Rules decide
Internal data rules often decide for you. If rules forbid data outside the building, your own server is the only option. If not, cloud is faster.
6. Cost
Cloud is paid monthly, by use. Your own server is a licence purchase plus upkeep. For small teams cloud is often cheaper; for large, stable ones, purchase can be better.
7. Recommendation
Without an IT team and without rules forbidding cloud, start with cloud. With data rules or an existing server, choose your own. The base is kept in both cases.
RULE OF THUMB: Data rules before budget. If data must not leave the site, cloud is not an option regardless of price.