A seal weld is provided for "additional leak tightness only". Often times for seal welds, the tube is welded to the tubesheet without the addition of filler metal (although, filler metal is sometimes used, especially for some metallurgies like 410 stn. stl.) The tube normally projects beyond the face of the tubesheet 1/8". So, when the tube is welded, it melts and fuses to the tubesheet. The tube hole in the tubesheet is not beveled for a seal weld.
A strength weld is provided "to carry longitudinal tube loads", and it also provides additional leak tightness. The procedure is essentially the same as a seal weld, except the tube hole in the tubesheet is beveled (ie. 45 deg bevel or j-groove) to allow filler metal to be deposited. Generally, this is a 2-pass weld.