Main Difference
The main difference between Dimension and Measurement is that the Dimension is a minimum number of independent coordinates needed to specify any point within a mathematical space and Measurement is a process of assigning numbers to objects or events.

Dimension
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it – for example, the point at 5 on a number line. A surface such as a plane or the surface of a cylinder or sphere has a dimension of two because two coordinates are needed to specify a point on it – for example, both a latitude and longitude are required to locate a point on the surface of a sphere. The inside of a cube, a cylinder or a sphere is threedimensional because three coordinates are needed to locate a point within these spaces.
In classical mechanics, space and time are different categories and refer to absolute space and time. That conception of the world is a fourdimensional space but not the one that was found necessary to describe electromagnetism. The four dimensions of spacetime consist of events that are not absolutely defined spatially and temporally, but rather are known relative to the motion of an observer. Minkowski space first approximates the universe without gravity; the pseudoRiemannian manifolds of general relativity describe spacetime with matter and gravity. Ten dimensions are used to describe string theory, eleven dimensions can describe supergravity and Mtheory, and the statespace of quantum mechanics is an infinitedimensional function space.
The concept of dimension is not restricted to physical objects. Highdimensional spaces frequently occur in mathematics and the sciences. They may be parameter spaces or configuration spaces such as in Lagrangian or Hamiltonian mechanics; these are abstract spaces, independent of the physical space we live in.

Measurement
Measurement is the assignment of a number to a characteristic of an object or event, which can be compared with other objects or events. The scope and application of measurement are dependent on the context and discipline. In the natural sciences and engineering, measurements do not apply to nominal properties of objects or events, which is consistent with the guidelines of the International vocabulary of metrology published by the International Bureau of Weights and Measures. However, in other fields such as statistics as well as the social and behavioral sciences, measurements can have multiple levels, which would include nominal, ordinal, interval and ratio scales.Measurement is a cornerstone of trade, science, technology, and quantitative research in many disciplines. Historically, many measurement systems existed for the varied fields of human existence to facilitate comparisons in these fields. Often these were achieved by local agreements between trading partners or collaborators. Since the 18th century, developments progressed towards unifying, widely accepted standards that resulted in the modern International System of Units (SI). This system reduces all physical measurements to a mathematical combination of seven base units. The science of measurement is pursued in the field of metrology.

Dimension (noun)
A single aspect of a given thing.

Dimension (noun)
A measure of spatial extent in a particular direction, such as height, width or breadth, or depth.

Dimension (noun)
A construct whereby objects or individuals can be distinguished.

Dimension (noun)
The number of independent coordinates needed to specify uniquely the location of a point in a space; also, any of such independent coordinates.

Dimension (noun)
The number of elements of any basis of a vector space.

Dimension (noun)
One of the properties that are regarded as fundamental measures of a physical quantity, such as mass, length and time.
“The dimension of velocity is length divided by time.”

Dimension (noun)
Any of the independent ranges of indices in a multidimensional array.

Dimension (noun)
An alternative universe or plane of existence.

Dimension (verb)
To mark, cut or shape something to specified dimensions.

Measurement (noun)
The act of measuring.

Measurement (noun)
Magnitude (or extent or amount) determined by an act of measuring.

Dimension (noun)
a measurable extent of a particular kind, such as length, breadth, depth, or height
“the drawing must be precise in dimension”
“the final dimensions of the pond were 14 ft x 8 ft”

Dimension (noun)
a mode of linear extension of which there are three in space and two on a flat surface, which corresponds to one of a set of coordinates specifying the position of a point.

Dimension (noun)
an expression for a derived physical quantity in terms of fundamental quantities such as mass, length, or time, raised to the appropriate power (acceleration, for example, having the dimension of length × time⁻²).

Dimension (noun)
an aspect or feature of a situation
“we must focus on the cultural dimensions of the problem”

Dimension (verb)
cut or shape (something) to particular measurements.

Dimension (verb)
mark (a diagram) with measurements.

Measurement (noun)
the action of measuring something
“accurate measurement is essential”
“a telescope with which precise measurements can be made”

Measurement (noun)
the size, length, or amount of something, as established by measuring
“his inside leg measurement”

Measurement (noun)
a unit or system of measuring
“a hand is a measurement used for measuring horses”