Although the terms walkie-talkie and two-way radio can be used interchangeably, some minor differences between the two technologies do actually exist. In a professional context, it is best to know which device you are referring to before you refer to it (but this is substantially less important on a day-to-day level).
Essentially, a walkie-talkie is the same as a two-way radio; there is no overt difference between the two. However, because there are so many different radios on the market, a distinction has arisen. The term walkie-talkie tends to imply a hobby model, or an otherwise cheap radio. Conversely, the term two-way radio tends to be more readily accepted in a business, as well as any equipment specific, context.
Walkie-talkies were invented around the time of the Second World War and were principally used by the military. Although they came in different forms, the most common version featured a large handset, which had a long antenna protruding from it. Modern walkie-talkies, on the other hand, feature a smaller design, typically with a rugged outer casing and a short aerial. They usually operate via a PTT (Push To Talk) button and available models vary in range from cheap childrens toys to professional, military grade equipment.
Generally, walkie-talkies are limited to only a few watts of power and a relatively short signal range. To this end, radio services often use a repeater (a device that increases range and boosts signal by squashing unused frequencies) in order to improve the walkie-talkies operation.
For their part, two-way radios, although they are also portable hand-held transceivers (a device that can both TRANSmit and reCEIVE messages) and they also use the PTT system, are slightly different.
A two-way radio is likely to have a stronger range and a harder outer casing. This is because the term two-way radio denotes a better class of product (usually).
Some two-way radios are also capable of sending and receiving messages at the same time; this is called full duplex An example would be a mobile phone, which employs two different radio frequencies at the same time. However, although a mobile phone is technically a two-way radio, the device is very different from what we understand as either a walkie-talkie or a two-way.
The most important distinction is that two-way radio almost always refers to professional, licensed equipment, whereas walkie-talkie more often describes unlicensed, consumer-grade radios.