I don't recall saying you were wrong, other than pointing out that “towards the Sun” isn't a constant direction; it is variable. And heliotropism isn't keeping the entire plant moving in one direction, it is twisting the leaves so that they face east in the AM and west in the PM.
And yes, if you put a grow light to the left of a plant, it will display Phototropism and grow (its stems) towards the light and to the left.
If you track the light from one side to the other over the course of a 12 hour period, the stems will still be growing towards the left due to its initial Phototropism; but its leaves will track the light as it moves because its (leftward growing) stems will twist to keep the leaves facing the light; this is Heliotropism.
If you move the light from the left of the plant to the right, its stems will start growing in the other direction and it will look like one confused plant!
Phototropism will point the plant stem/wood structure in the direction where it is getting the most sunlight; and Heliotropism will point the leaves towards the sun by causing the stems to twist through hydraulic pressure.
So I guess Phototropism is the long term strategy of growing the entire plant structure towards the sunlight; while Heliotropism is the day to day tactic of facing your leaves to the sunlight.
I.E. Plants and trees grow towards the maximum source of sunlight (following it by maintaining an average position with respect to it’s daily movement).
If the source of light is rigid, they grow straight for it.
The plant’s ability to use (or need to use) is likely miniscule, and may only be used in a very brief period when it is underground.
A seed sprouts due to moisture and temperature (change). The temperature change is a direct result of sunlight. The sprouting seed pursues the source of that warmth to reach the surface. In that case it may be following infra-red rather than visible solar.
The use of ‘gravity’ to determine direction of growth is an unproven theory, and seems to have very little effect compared to the source of heat and light.
If you can point me to a documented source which can prove that seeds use ‘gravity’ to determine direction, I would be glad to read it.