From AMS Glossary
According to some authors, the air of the doldrums or the equatorial trough, to be distinguished somewhat vaguely from the tropical air of the trade-wind zones.
Tropical air "becomes" equatorial air when the former enters the equatorial zone and stagnates. There is no significant distinction between the physical properties of these two types of air in the lower troposphere.
Grimes, A. 1951. Compendium of Meteorology. p. 881.