Can I have the same security Government Standards with Fedora than with RedHat?
In addition to the other answer, "Military grade" security often refers to set the configuration settings of the machine to specific approved settings "hardening". Given the military context, my guess is a requirement for FISMA configuration hardening. There are a number of different security benchmarks available. DISA and NSA are examples of agencies with their own configuration standards.
NIST's webpage "Managing Security Risk by Using Common Security Configurations" contains a number of different Federal security configurations that you can implement.
First, there is no such thing like "military grade security" except for marketing. And since this is not a protected phrase you'll find this claim often in products which primarily consist of shallow claims without providing adequate security.
My guess is that the "government standards" you refer to are actually certifications like Common Criteria or the approval for use inside a specific classification level like NATO restricted, top secret or similar. And this case the answer is that these certifications and approvals are only apply to the specific tested product version and do not apply to similar products. This means that any certifications for RHEL do not apply for CentOS although it is mostly the same and do not apply to Fedora which is already very different from RHEL.
And even if you use a product which got specific certifications or approvals you have to carefully read what is actually covered and how the product should be used in a certified/approved way. Usually only some functionality of the product is covered and only when used in a specific way or specific environments.