Chlorophyll content is a physiological trait that is part of the machinery needed to sustain a certain photosynthetic capacity. The processes leading to the synthesis of chlorophyll include responses to nitrogen and light availability. As the chlorophyll content per unit leaf surface area also depends on the number of mesophyll cells per surface area and leaf thickness, there is also a morphological trait related to the measurement which however is a result of the physiological adaptive responses to light, drought etc.
Chlorophyll content is a physiological parameter. However, in some publications you might find it under biochemistry category. In the past decades, the concept of plant physiology changed considerably, so you can read plant physiology papers from different time periods that seem to belong to different fields, in terms of studied parameters. Some old papers on plant physiology are found nowadays under plant ecophysiology field. For scientist working several decades ago the plant physiology papers from nowadays would appear as purely biochemistry work. All parameters referring on processes, functionality and dynamics should be considered physiological. Indeed, there is always a biochemical involved mechanism.
Chlorophyll content is a physiological parameter, But what the instrument (SPAD) measures is not the chlorophyll content. it should be determined by a proper biochemical method.
Basically, chlorophyll is a pigment and it plays an important role in the photosynthetic capacity and ultimately it influences the plant stand and productivity of the plant species. Hence, measurement of chlorophyll content means measuring the physiological traits of the species.
SPAD index indicates only the greenness of leaves. In most cases it agrees with the chlorophyll content. But under saline conditions, there is a revers relationship between them.In this case, the SPAD doesn,t classified in physiological traits, it shows only the greenness color, so, it is a morphological trait.