Hold, grip, grasp, clutch are comparable when they denote the power of getting or of keeping something in possession or under control.
Hold is the most comprehensive of these terms, for it may apply to material, immaterial, or intangible matters and may imply mere possession or control or possession and control securely maintained.
Grip primarily implies the power of taking hold of by the hand, but in its secondary senses it definitely suggests a firm and tenacious hold (as on a country by an oppressor, on a person’s system by a disease, or on a body of facts or principles by an eager mind).
Grasp implies the power to reach out and get possession or control of something; in its basic applications it may be distinguished with difficulty from grip, but in its now more common extended applications especially to what can be possessed by the mind it frequently distinctively connotes remarkable powers of comprehension on the one hand or outstanding range of mastery on the other.
Clutch basically implies a seizing and holding with the avidity or rapacity of or as if of a bird of prey. In its extended use it stresses, far more than any of the preceding nouns, the notion of control as distinguished from possession or that of the act or fact of grasping with violence, with effort, or with frantic determination (as under the impulsion of terror).