Gaia is a software running on appliance (virtual-physical) just like ASA/FTD. You can install ASA/FTD on cisco appliances. Cisco Adaptive Security Appliance (ASA) Software is the operating system for the cisco ASA family. It delivers enterprise firewall capabilities for ASA devices in an array of form factors -standalone appliances, blades, virtual appliances- for any distributed network environment. Cisco Firepower Threat Defence (FTD) is a unified software image, which includes asa features and FIREPOWER features. FTD can be deployed on cisco firepower series appliances and ASA series appliances.
Check point GAIA is the next generation secure operating system for all check point appliances, open servers and virtualized gateways. Check point provides all sizes appliances for data center, enterprise, small business&brach office etc. But appliance names do not start with gaia like ASA -X firewall. That's not mean check point has no physical hardware appliance. The Gaia supports the full portfolio of check point software blades, gateway and security management products. Just like Maik Dummer said, you can read appliances brochure from the check point web site.