The difference between Rampant and Unrestrained

When used as adjectives, rampant means rearing on both hind legs with the forelegs extended, whereas unrestrained means immoderate.

check bellow for the other definitions of Rampant and Unrestrained

Rampant as an adjective (originally):

Rearing on both hind legs with the forelegs extended.
Rampant as an adjective (heraldry):

Rearing up, especially on its hind leg(s), with a foreleg raised and in profile.
Rampant as an adjective (architecture):

Tilted, said of an arch with one side higher than the other, or a vault whose two abutments are located on an inclined plane.
Rampant as an adjective:

Unrestrained or unchecked, usually in a negative manner.
Rampant as an adjective:

Rife, or occurring widely, frequently or menacingly.

Unrestrained as an adjective:

immoderate; not restrained or held in check

Examples:

"The party was a scene of unrestrained debauchery."
Unrestrained as an adjective:

spontaneous, natural and informal; unconstrained

Examples:

"Their meeting was one of unrestrained joy."
Unrestrained as an adjective:

Not subject to physical restraint.