1)Salesforce is a Customizable CRM .You are right here .Salesforce CRM is considered as a SAAS .Lot of functionality needed for a Sales Application are provided outofbox .Salesforce also is a PAAS(FOrce.com Platform of Salesforce is a PAAS) so you have components available to further build your business logic . Declarative components are validations ,roles ,profiles ,workflows ,Approval Process ,page layouts ,record types while you can further customize the application using code triggers,apex and Visualforce
2)ServiceForce I haven't heard but service cloud consists of components for Case Management preferably it consists of components to build applications needed to manage Callcenter and Customer Support .There are important feature licence like Live Agent,knowledge which help to develop and configure applications needed for Call Center Industry
3)SalesCloud provides objects and components necessary to build Applications which can be used in Sales Process .There are outofbox objects provided to manage sales cycle right from Marketing Stage (Campaign to Opportunity and Quote Management )
4)The Salesforce1 Platform brings together Force.com, Heroku, and ExactTarget into one family of cloud services — all built API first — to help deliver apps that connect products, users, and next generation experiences. Designed for scale and speed, it provides a fast way to build apps with open APIs, back-end services, integration tools, starter templates as well as powerful developer environments; there’s no limit to what you can build.
Again dont get confused with Salesforce 1 App(Its different from Salesforce 1 Platform) that you can download from Appstore or Google Playstore for Android .Salesforce 1 App is an in house mobile application that will provide some of the functionality that you see in your desktop App.Most of the objects and features that you have build for desktop can be easily tailored with help of this application and you can have a Mobile Application for your Enterprise Business without much effort and not worrying about packaging .
If salesforce 1 don't tailor to your needs Salesforce provides SDK to build native ,hybrid as well as HTML5 application which you can package .
5)Appexchange applications are built by ISV vendors and Salesforce Developers where an application is marketed either for free or for cost to avoid build of an application from scratch .These Apps are available on appexchange site of salesforce and you can download and Install on your Instance and achieve your functionality without worrying about development .