EXTEND

change : I don't use this, but this is from the link at the bottom of this post "Here’s an OLD SCHOOL trick. Instead of using TRIM or EXTEND, try using the CHANGE command. Enter the command CHANGE, select the endpoints of the objects to Extend or Trim (with a window crossing or fence), turn your Ortho ON, and then select the point where you want the endpoints of the objects to go. Now, just for fun, try turning the Ortho OFF and see what happens!"

lengthen : er, lengthens an item.... you can select a point and then another to lengthen to or a discrete measurement (via the keyboard).

solid edit : no idea I'm only 2D!! but guess that it's to do with extrusion...

stretch : really useful, allows you to stretch an item...  you can pick a point and stretch it to another, making the "crossed" items shorter or longer, depending on where the item is being moved to..

trim : select a cutting line or lines and then trim to the next cutting line or lines

edge : it's very similar to the projection option...

project : allows you to extend items to a projected intersection, i.e. a line that it doesn't necessarily intersect with but would if that line had been extended.


TRIM

fence : useful if you want to extend or trim a number of items to the same line..  you don't have to select them all, you just select two points and all the items between those two points are extended or trimmed..

crossing : allows you to quickly select multiple items.. (here, as I don't use 2006 onwards :( http://lynn.blogs.com/lynn_allens_blog/2005/04/autocad_2006_tr.html)

project : (see above)

edge : (see above)


see here http://www.dailyautocad.com/autocad/hip-tip-multiple-extend-and-trim-by-using-fence-option/ for some good examples of the above.

also see here : http://lynn.blogs.com/lynn_allens_blog/2007/01/happy_new_year.html

Don't forget there are about 9 different ways to do the same thing in AutoCAD and no way is the "right way" but there are probably some "wrong ones" - i.e. those that take way too much time to do!!

HTH