The differences within each of these groups are small, and often ignored by manufacturers. While many of these technically come in closed cell and open cell foams, RC users are only interested in the closed cell versions.
- EPS Expanded Polystyrene (styrofoam, 'cooler foam')
Ubiquitous packing and insulation material until biodegradable alternative popped up in recent years, but still very common and the only type of foam the average person is likely to be familiar with. Mostly supplanted by EPO and some EPP, this is still commonly used for big flying wings and by scratchbuilders. Lightweight, but somewhat brittle - it will bend until the tension becomes too much and then a fracture will snap through. If building with EPS as a landing surface, expect to need to tape or glass the surface to protect against chunks being gauged out, which will make this much, much stronger. EPS is apparent from the grain and sometimes the complex shapes: pebble-sized chunks are used to fill a mold, and then heated to expand them by a factor, which presses them together until they're one mass.
- XPS Extruded Polystyrene (Bluecor / Blue Foam / FFF ("Fan Fold Foam"), Pink Foam, Insulation Foam)
A slightly stronger, denser version of EPS formed into sheets. Notable due to its much smaller grain size than the big chunks of EPS. In the United States, this is sold very inexpensively as building insulation at the major hardware superstores: blue in the form of an accordion/fan bundle at Home Depot, and pink at Lowes & elsewhere.
Styrofoam is technically a trademarked name for XPS, but in the US it has become a generic trademark for all polystyrene foams, the most common of which are EPS.
- Foamboard (Dollar Store Foam)
A thin layer of expanded polystyrene foam covered by paper, which can be removed with alcohol or warm water to make this waterproof. It is not uncommon to build up wings out of this material, though it is somewhat weak without reinforcement.
Depron comes in EPS and XPS, but the one commonly used in the RC community is a high-density XPS that comes in very thin (3-5mm) sheets as a covering and layering material with a smoothed surface. It is not uncommon to build up wings out of this material. The most common place you're likely to find Depron is 'styrofoam' food containers. This tends to be specifically marketed towards RC users at a significant price, but the XPS insulation foam needs prices low enough for bulk construction use, so it is likely to be a lot cheaper if one is able to hot wire cut and sand their wing anyway.
 Polypropylene / Polyolefin / Blends
The reputation appears to be that most blends sold as EPP are somewhat heavier than polystyrene, but that the 'EPO' labelling (technically polypropylenes are part of a class called polyolefins) brings the weight back down with some slightly different mix - with dubious factual support.
A slightly less stiff, *much* less brittle and stronger alternative to polystyrene. Will bend a bit more easily for the same thickness, but refuses to break. The most common product the average person has encountered this in will be either the really strong non-squeeky packing foam edge-pieces, or the "pool noodle" water toys. Regrettably difficult to procure useful-sized pieces in a retail store.
While a manufacturer could technically label all EPP to be EPO, the frequency with which this occurs is unknown. The RC community's best guess is that this is usually polystyrene beads in a matrix of EPP. This would be a more economical and lighter-weight alternative to pure EPP, and it has become the RC industry standard for building pre-molded foam planes.
This is a dominant insulation material in commercial roofing applications and popular elsewhere, so it's widely available, but is not recommended for building planes out of. More brittle than EPS and often full of glass fibers, which makes sanding a hassle due to problems with eye, skin, & lung exposure. May come in blue stacks, similar to Dow Blucor fan fold foam.