I have been using automation testing tools and have developed automation frameworks, giving you the details based on my experience -
Automation testing Tool -
Its a utility which can have features, functions and capabilities to operate on a specific or variety of Application under test (AUT)- such as - it can search and uniquely identify AUT objects, panes, button, links etc.
the underlying Libraries, utilities, methods and object identifying model work as a core framework for tool, which provides features, functions and capabilities to operate it.
But this underlying core system is mostly propitiatory /static code and cant be changed as per custom needs.
most of the market standard tools focus on their object recognition model with a vast list technologies like .NET, JAva, Struts, etc. but may not be equally strong or capable in -
Creating test scripts / scenarios
Data input and usage of data files such as text, excel, Json, XML etc.
Managing scripts execution
with a Basic result reporting capabilities.
most of the time the lack the customization and adaptation option - as every project or work has different need.
Automation framework -
Framework are as a word means - set of rules or best practices. even though a Automated testing tool has a features and capabilities, it requires a set of rules and driver to initiate, manage and report a complete test execution.
A Framework can be a set of scripts ( libs, jars, methods etc.) which are developed with a customized and tailored client / project / work needs. It can use the core / best features and functionalities of automation tool's core functionalities which then wrapped with the framework - to create a -
more seamless multi script and platform execution.
test data management - creation, input and reset if requires.
test orchestration -
what triggers the build, where the inputs comes from, what all to execute, where to execute, how to integrate, who / how to control execution, where to reporting and whom to alert.
Hope this give a bit more prospect to this question.