A node is a coordinate location in space where the degrees of freedom (DOFs) are defined. The DOFs for this point represent the possible movement of this point due to the loading of the structure. The DOFs also represent which forces and moments are transferred from one element to the next. The results of a finite element analysis (deflections and stresses), are given at the nodes.
In the real world, a point moves in six different directions: translation in X, Y, and Z, and rotation about X, Y, and Z. In FEA, a node can be limited in the calculated motions for various reasons. For example, there is no need to calculate the out of plane translation on a 2D element. It is not a 2D element if its nodes can move out of the plane.
The DOF of a node relates what types of forces and restraints are transmitted through the node to the element. A force, axial or shear, is equivalent to a translation DOF. A moment is equivalent to a rotational DOF. Thus, to transfer a moment about a certain axis, the node must have a rotational DOF about the axis. If a node does not have that rotational DOF, then applying a moment to the node has no effect on the analysis. This can impact how two parts are connected together. Additional modeling can be required to insure that the connection between the parts does not produce a hinge. See the page Meshing Overview: Mesh Overview: Creating Contact Pairs: Examples of Contact for examples.
Likewise, restraining that node with a rotational boundary condition has no effect if the node lacks the ability to transmit the moment. Placing a boundary condition of Tx Ty Tz Rx Ry Rz on a node of a brick element is equivalent to applying a Tx Ty Tz boundary condition; the brick element node does not calculate the rotations.
An element is the basic building block of finite element analysis. The type of element for the analysis depends on the type of object to model and the type of analysis to perform.
An element is a mathematical relation that defines how the degrees of freedom of a node relate to the next. These elements can be lines (trusses or beams), areas (2D or 3-D plates and membranes) or solids (bricks or tetrahedrals). It also relates how the deflections create stresses.