Crow's Feet Notation is one of several Entity Relationship diagramming notations.
An entity–relationship model is the result of using a systematic process to describe and define a subject area of business data. It does not define business process; only visualize business data. The data is represented as components (entities) that are linked with each other by relationships that express the dependencies and requirements between them, such as: one building may be divided into zero or more apartments, but one apartment can only be located in one building. Entities may have various properties (attributes) that characterize them. Diagrams created to represent these entities, attributes, and relationships graphically are called entity–relationship diagrams.
An ER model is typically implemented as a database. In the case of a relational database, which stores data in tables, every row of each table represents one instance of an entity. Some data fields in these tables point to indexes in other tables; such pointers are the physical implementation of the relationships.
And more specifically
Crow's foot notation is used in Barker's Notation, Structured Systems Analysis and Design Method (SSADM) and information engineering. Crow's foot diagrams represent entities as boxes, and relationships as lines between the boxes. Different shapes at the ends of these lines represent the cardinality of the relationship.
Object diagrams are a slightly different from ER diagrams.
In the Unified Modeling Language (UML), an object diagram focuses on some particular set of objects and attributes, and the links between these instances. A correlated set of object diagrams provides insight into how an arbitrary view of a system is expected to evolve over time. In early UML specifications the object diagram is described as:
"An object diagram is a graph of instances, including objects and data values. A static object diagram is an instance of a class diagram; it shows a snapshot of the detailed state of a system at a point in time. The use of object diagrams is fairly limited, namely to show examples of data structure."
The latest UML 2.5 specification does not explicitly define object diagrams, but provides a notation for instances of classifiers.
Object diagrams and class diagrams are closely related and use almost identical notation. Both diagrams are meant to visualize static structure of a system. While class diagrams show classes, object diagrams display instances of classes (objects). Object diagrams are more concrete than class diagrams. They are often used to provide examples or act as test cases for class diagrams. Only aspects of current interest in a model are typically shown on an object diagram.
If you are using a UML modeling tool, you will typically draw object diagrams using some other diagram type, such as on a class diagram. An object instance may be called an instance specification or just an instance. A link between instances is generally referred to as a link. Other UML entities, such as an aggregation or composition symbol (a diamond) may also appear on an object diagram.