Classic Profile in aem

I assume you have the pom.xml similar to this sample https://github.com/adobe/aem-guides-wknd/blob/main/core/pom.xml 

Cloud profile specifies the dependency of Cloud API Jar package. 

<dependencies>
                <dependency>
                    <groupId>com.adobe.aem</groupId>
                    <artifactId>aem-sdk-api</artifactId>
                </dependency>
            </dependencies>

More info on API jar dependency: https://experienceleague.adobe.com/docs/experience-manager-cloud-service/content/implementing/developing/aem-as-a-cloud-service-sdk.html?lang=en 

Classic profile specifies adds more dependencies required non cloud AEM deployments. it also have plugin execution configurations for Maven Bundle plugin on what is to include/import or Not import packages during the execution of build lifecycle. It all depends on what you have in your pom.

More info : https://felix.apache.org/documentation/subprojects/apache-felix-maven-bundle-plugin-bnd.html 

Sample: 

<build>
                <plugins>
                    <plugin>
                       <!--================
                        Relax AEM 6.x Dependencies to allow for broader deployment compatibility for 6.5.x
                        ====================-->
                        <groupId>biz.aQute.bnd</groupId>
                        <artifactId>bnd-maven-plugin</artifactId>
                        <executions>
                            <execution>
                                <configuration>
                                    <bnd><![CDATA[
        Import-Package: javax.annotation;version=0.0.0, 
                        com.day.cq.search;version="[1.3.0,2)", 
                        com.day.cq.wcm.api;version="[1.27.0,2)", 
                        org.apache.commons.lang3;version="[3.9.0,4)", 
                        org.apache.sling.api.resource;version="[2.11.1,3)", 
                        *
                                        ]]></bnd>
                                </configuration>
                            </execution>
                        </executions>
                    </plugin>
                </plugins>

Hope this helps!