Heading 070 means turn until your heading indicator shows you facing 70 degrees magnetic. Different types of airplanes use different types of heading indicators, but they all show magnetic headings.
Radial 070 is a bit more complicated. I'll assume that you don't know much about VOR stations in the following explanation, if you do know much about it, overlook what you already know
A VOR station is basically a radio transmitter. A typical station, physically, is a low, round building, with a large cone shaped antenna sticking up out of the center, and a series of small antennas around the top perimeter of the building.
VOR stands for VHF Omnidirectional Range. The VOR station projects (transmits) straight line courses (radials) in all directions. Imagine a bicycle wheel, the VOR station is the hub, and the radials are the spokes (though in reality there are infinatly many radials).
For navigation purposes, we are only concerned with the radials that correspond to whole degrees, and we number them starting with 1, which is the radial that goes away from the VOR in the direction that is 1 degree east of magnetic north. We then number each radial according to it's corresponding degree value (from magnetic north).
Therefore, radial 070 is the radial that has a direction 70 degrees east of magnetic north, starting at the VOR station and proceeding away from it.
Hope this makes sense and is helpful