You might try using the definition from any one of the states DEC Stormwater Manuals. I use NY's manual regularly
http://www.dec.ny.gov/docs/water_pdf/swdm2015entire.pdf
Retention Ponds - aka wet ponds, retain water - meaning there is ALWAYs some amount of water in them. This means you either have soils with no infiltration, a liner, or in the case of a pocket wetland your pond is in the water-table.
Detention Ponds detain meaning they hold water temporarily. You can have detention with or without infiltration. Without infiltration means your detention pond will need to have a drain (either under drains or an outlet pipe).
Infiltration Basins is a type of detention pond have to have soils with a minimum infiltration rate (for most it is 0.5"/hr) and will help recharge the water-table. It will typically also have some sort of staged storage device to let water out at pre-developed flow rates or at the very least an emergency spillway.
I hope that is helpful. If you have more questions feel free to ask. Stormwater management can easily snowball in its complexity so don't be discouraged if it takes a minute to follow all the different branches.
-Emiy