I think that you got a bit confused about terminology. In fact Chemotrophic is an organism that obtain energy by organic or inorganic molecules.
In your case I think that you want to know the difference between Chemotropism and Chemotaxis.
Chemotropism
Chemo-tropism is the growth of organisms (or parts of an organism, including individual cells) such as bacteria and plants, navigated by chemical stimulus from outside of the organism or organisms part [...]
An example of chemo-tropic movement can be seen during the growth of the pollen tube, where growth is always towards the ovules.
Chemotaxis
Chemotaxis (from chemo- + taxis) is the movement of an organism in response to a chemical stimulus.Somatic cells, bacteria, and other single-cell or multicellular organisms direct their movements according to certain chemicals in their environment. This is important for bacteria to find food (e.g., glucose) by swimming toward the highest concentration of food molecules, or to flee from poisons (e.g., phenol). In multicellular organisms, chemotaxis is critical to early development (e.g., movement of sperm towards the egg during fertilization) and subsequent phases of development (e.g., migration of neurons or lymphocytes) as well as in normal function.
Hence, to sum up (Chemo)taxis is the physical movement of a cell (or an organism) in response to a (chemical) stimulus, as done by the Antherozoids that are attracted towards Archegonia. However (Chemo)tropism is the growth on organism toward a (chemical) signal, like done by Spermatophytes where pollen tube moves (so it growths) towards the Ovule.
Hope this explanation help you to clarify.
