I can't explain it well, the diference is simple wen we spell about decibels we are spealling about a logaritmic scale, but wen we spell about DBA we are refering to a phisic unit an their scale mode(0 DBA = is a presure of 0.2 nanobars), we can refer it to DB, but this can make confusion for this I used the DBA name, both are corrects but this is more clear.
read this explanation, is very simple but veri good: http://www1.jaycar.com.au/images_uploaded/decibels.pdf
this is a more estense explanation:
http://www.jsdsound.com/decibels.htm