What is the difference between After Effects and Premiere Pro although they're both Software media editing tools?

 Adobe Premiere is for video editing  and After Effect for motion graphics .

the options in premiere are limited for adding some motions to the video ,and the options in AE are limited for editing a video and take so much time.though you can do a graphic motion in AE and add it to your video in Pr.  

Asking the difference between After Effects and Premiere is like asking the difference between Word and Excel. Word is for word processing and Excel is for spreadsheets. Sure, you can write a letter in Excel and you can create tables and cells in Word to look like a spreadsheet, but why would you want to? They're very different products intended for very different uses. Same thing with Premiere and After Effects. Dave said it right. You edit video and audio in Premiere. You do compositing and motion graphics in AE. There are a bunch of effects in Premiere that can do some compositing and you can do quite a bit as far as motion graphics go, but it's nothing like what you can do in AE.

Premiere is software for editing (like Final Cut or Vegas...) while After Effects is a post production based package, meaning work on compositing and 2D video effects on existing video footages + its used for motion graphics art.

after effects = post production (compositing film and video)

set replacement

set extension

grain matching

rotoscoping

visual effects

match moving

video stabilization

Premier Pro = production (video editing)

editing

color correction

color grading

sound and video mixing