In a nutshell, Civil Engineers are involved in building projects, and Environmental Engineers are involved in cleaning up the messes (i.e. hazardous waste) left behind.
A lot of people who work in environmental engineering do not come from a civil engineering background, typically, the only thing required to be hired by industry is the 40 hour Health & Safety training class.
Training Curriculum Guidelines - (Non-mandatory) - 1910.120 App E
A lot of the environmental work done by environmental engineering consultants involves regulatory compliance, especially with regard to preparing stormwater reports, Phase I and Phase II soil contamination reports, Environmental Impact reports, toxic release inventories, and chemical spill cleanup plans. There are myraid regulatory agencies involved, different government entities are involved in air regulations, water regulations, and so forth, so environmental engineers need to be familiar with regulatory and permitting requirements from city, county, state and federal agencies.