Wondered that as well. From the info below it seems, 'not much difference at all'.
Some info below:
The gastrocnemius is the larger of the two major calf muscles and it gives shape to the rear lower leg. It is located at the top back of the lower leg and it extends from the knee joint to the ankle joint. It is composed of two heads (medial and lateral) that lie next to each other. The gastrocnemius can be easily seen when it is well developed and accompanied with low body fat. This muscle portrays that well-known diamond shape or the appearance of an upside down heart.
The gastrocnemius is best targeted with straight legged-heel raises, such as donkey calf raises and standing calf raises. Some people put a slight bend in their legs to relive some pressure, but this will only target the soleus more, putting less emphasis on the gastrocnemius. If you are going to train the gastrocnemius, lock your knees to target it solely. Don?t bring other muscles into play.
Donkey raises are superior to standing calf raises due to the position it puts you in. The gastrocnemius ties in with the hamstrings at the back of the leg. When you are in the bent over position, the hamstrings and gastrocnemius are stretched out, giving the donkey calf raise an advantage over standing calf raises, due to the intensity and localization.
The gastrocnemius muscle responds well to heavy poundage, using more sets and fewer repetitions, due to the great number of fast-twitch (white) muscle fibers.
The soleus is the smaller, yet slightly wider, of the two major calf muscles. It is not visible because it lies under the gastrocnemius. The soleus muscle gives width to the back of the lower leg.
The soleus comes into play in many endurance activities. The gastrocnemius usually has a lot of fast-twitch muscle fibers or an equal number of fast and slow-twitch fibers. This allows the soleus to take over in many cases when the gastrocnemius becomes fatigued.
The soleus can be best trained with any bent-knee exercises, such as seated calf raises. The gastrocnemius is not strongly involved in this movement.
The soleus responds well to light weight, fewer sets, and more repetitions since it is composed mainly of slow-twitch muscle fibers (red).
The anterior tibialis is located at the front portion of the lower leg. A well-developed anterior tibialis adds more depth and symmetry. It will make your calves appear larger from the front and side.
This overlooked muscle can be best trained with toe raises. Simply place the heel of your foot on a platform, such as a weight plate placed on the floor. Place a dumbbell across your foot and raise your toes as high as you can in a controlled fashion. Lower and repeat.
Gastrocnemius - donkey calf raises and standing calf raises
Soleus - seated calf raises
Tibialis - toe raises
And another source:
"Data indicated that there was no significant difference between the main exercise effects on the gastrocnemius for the donkey calf raise (80) percent) and the standing one-leg calf raise (79 percent). There was, however, a significant difference between the main effects for those two exercises and the standing calf raise (68 percent) and the seated calf raise (61 percent).
The results show that donkey calf raises and standing one-leg calf raises produce the greatest amount of muscular electrical activation for the gastrocnemius. Although there's no significant difference between the two exercises, donkey calf raises still produce 1 percent more activation.
% EMG Max
1) Donkey calf raises
2) Standing one-leg calf raises
3) Standing calf raises
4) Seated calf raises