Welcome
Balduvia!
To answer your question, in brief, PS Elements is "Photoshop Lite," acutally a more powerful version than the old Photoshop LE. It's meant for the amateur or beginner, focussing mainly on importing and correcting digital photos. Its reason for being seems to be to make simple photo correction easy for those who don't need the full power of Photoshop itself.
Photoshop itself is a very powerful, complex program meant for professionals or those who want to go there

Yes, there is a huge price difference.
To find out more, a good start is at
Adobe's site. Check out both Photoshop & Elements and compare, the decide what you need.