Pattern: is a repeated use if the same element  to create an overall design pattern. It is widely use in Architecture, decorative arts, textiles, graphic arts. Plus it can also be use in painting and drawings.

Motif: is an element of a pattern, image or shape, which is required in design. It may repeat in a design or composition, often many times or may just occur once in a work.
Design process is the activity of making a motif.

Motif can be created from simple shape. They can be regular or irregular.
Regular shapes include circle, triangle, square, oval, and others. Shapes
can be combined to form patterns.

A key to figuring out the pattern puzzle is to "see" its repeating element (unit) and the logic behind the sequence.

Types of patterns

Organic patterns: Shapes and curves are found in nature repeated to create an "area". 

Geometric pattern: Repeating lines, Shapes and angles as found in human world.

Radial pattern: Repeating elements that all share the same center.

Categories of pattern

Random

Irregular repeat

The motifs are arranged in many styles of the surface. This means that there is no specific flow even through the same

motif has used to create a pattern. This again called random repeat.

Planned

Planned patterns can be:

ROW (linear)

GRID

CENTER / RADIAL

Examples

linear

Grid

Radial

Grid patterns can be:

Basic

Full repeat: The motif is repeated regularly in each square/rectangular space.

Alternating

In regular repeat patterns, the motif used can alternate repeat patterns. In alternate repeats, there can be two motifs, which combine

to form a repeat as shown below.

Half drop repeat: A grid is made such that the subsequent row of squares

drop half way as shown below.

Textile design example