Wings Level vs HDG Sel
 

When we press TOGA, we have to variations

Option 1 - Flight director commands wings level on takeoff.

Option 2 - Flight director commands HDG SEL on takeoff.

Why have two variations? Also what is is the advantage of one over the other?:

ugh:

Where you find that option?

There are two Variations in the B737NG.

Option 1 Wings Level.

Option 2 HDG SEL.

If I understand the system manual correctly, these are not selectable options, in other words, your airplane has either one mode or the other. The only advantage to the wings level command that I can see would be that if you botch a V1 cut something fierce, the FD will at least guide back to wings level.

Automatic Flight

The planes I fly have the option to preselect HSEL, which engages at 400ft.
They take off in "wings level".
Never heard of HSEL engage at TOGA in Take Off.
Could lead to interesting maneuvers..

Wings Level vs HDG Sel
 

I know I'm not on the 73, but our procedure is to take off in HDG mode. Our logic is, pretty much all contingency procedures start off from runway heading anyway, and you should be getting wings level if you are correctly aligned prior take off clearance.

We used to have both options in our fleet. However on changing over to LNAV/VNAV take off it changed on all aircraft to HDG SEL during take off until LNAV automatically kicks in at 50ft. Roll authority is limited to 8° bank in HDG SEL.

Upon having a close look at available options, you are right, B737NG and Denti. And at 400 ft the 8 degree limitation is removed.
However, the HSEL is only active upon lift off.

Although never saw that option.

Never too old too learn I guess.