In addition to the @Paul and @Berin answers, which are very correct and concise.
Now I've searched what is the meaning of REST server and REST client
but I could not find a good answer. Could someone explain them?
The short answer is
A little bit longer answer is
RESTful server (applications) are applications capable to provide us with resources and management of these resources on the WWW employing the HTTP specifications as communication protocol.
RESTful client (applications) are applications capable to consume and operate with resources exposed by RESTful servers, under the same premises.
In layman's word,
- RESTful applications are those that totally embrace the WWW architecture features.
Leonard Richardson and Samy Ruby came up with an architectural style that embraces all these premises and constraints. Resource Oriented Architecture (book). Its interpretation of REST applications (APIs and services) has been broadly adopted by the community and has promoted the proliferation of books, blogs and articles regard this topic. Having in common all of them, the Fielding dissertation.
Disparity of RESTful implementations
Out there, in the wild market of the RESTful applications, we will see applications claiming to be RESTful when the truth is that they don't totally accomplish with the Fielding's constraints.1
Accomplishing all the architectural constraints of REST is not exempt of tradeoff. The community has had to adopt a certain degree of flexibility at the moment of implementing these constraints. As usual, it's a matter of suitability and cost-benefit.
Among the constraints, the Uniform interface stands out from the others. This constraint is especially relevant because is the one that makes us employ the HTTP semantics and contents for representing our business (services, models, etc) in a RESTful way.2
Each implementation of REST differs notably from project to project and from provider to provider. It's understandable since each of them has to deal with different requirements, needs and resources. Ultimately, requirements and needs prevail over the rest.
1: Does it means they are not RESTful? Well, that's open to debate and opinions. Both things off-topic here.
2 : An example of its relevance is the large number of articles, guides or questions in SE and SO about how to successfully implement the URIs, Http Methods, Http Status, etc; to meet successfully the expectations of the business.