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Motion graphics is the process of creating a series of images, text or other elements that form a coherent whole, while motion design is the creation of three-dimensional objects used in motion graphics.
Yes, you can use .mogrt files without After Effects. You can create graphics in Premiere Pro using the Essential Graphics panel and then export them as .mogrt files for sharing or reuse.
To open a Motion Graphics template in After Effects, select a composition from your project and add it to the Essential Graphics panel. To open the current composition, select Composition > Open in Essential Graphics.