We use ‘e-assessment’ to mean different things, but we also use a variety of terms to describe e-assessment!
We have CAA (computer-aided assessment), or is it CAA (computer-assisted assessment); CMA (computer-marked assessment), or is it CMA (computer-mediated assessment).
Becoming a little more specific, the term online assessment implies that students are not simply using a computer, but working online. At the Open University we use iCMA (interactive computer-marked assignment) to distinguish the interactivity of iCMAs from something which is simply submitted electronically or something which may be marked electronically, but without instantaneous feedback and the provision of a second and third attempt.
Technology-enabled assessment (or is it technology-enhanced assessment) includes other technologies, like Learnosity‘s use of mobile phones in assessing spoken language skills.
Well that’s my understanding anyway. Please do feel free to disagree with me or to add other terms!