Camel is smart routing and mediation engine which implements the Enterprise Integration Patterns and is designed to be used either inside an ESB like ServiceMix, in a Message Broker like ActiveMQ or in a smart endpoint or web services framework like CXF. ServiceMix is an ESB, a JBI container and an integration platform. So they both address different needs though they are both designed to work great together.
Camel can be deployed as a component within ServiceMix to provide EIP routing and mediation between existing JBI components together with communicating with any of the other Camel Components along with defining new JBI components on the NMR. So Camel is similar to the ServiceMix EIP component.
To work with Camel and ServiceMix you take your Camel Spring configuration and turn it into a JBI Service Unit using the maven plugin or archetype. For more details see ServiceMix Camel plugin.
So you could start out using Camel routing inside your application via Java or Spring; then later on if you choose to you could wrap up your routing and mediation rules as a JBI deployment unit and drop it into your ServiceMix ESB. This provides a nice agile approach to integration; start small & simple on an endpoint then as and when you need to migrate your integration components into your ESB for more centralised management, governance and operational monitoring etc.