Well, they are similar in that the motion of oscillation is perpendicular to the motion of the wave. Think of a surface wave on water for example. The water only goes up and down but the wave travels outward. A lateral wave is analogous to waving a rope back and forth. The rope only moves left and right but the wave travels outward.
Both of these are transverse waves.
The rope is however a good analogy because it demonstrates another phenomenon.
Polarisation.
In wave terms (this has nothing to do with charges and ions) it simple means that the wave particles are constrained to only vibrate in certain positions.
You can waggle the rope up and down or side to side (lateral waves), or if you are clever at any angle to the horizontal you chose.
This is an example of plane polarisation, the rope is constrained to waggle in a vertical, horizontal or intermediate plane.
If you now start rotating the rope in a circle, like a skipping rope, and at the same time waggle it up and down, the up and down waggle transmits as a helix down the line.
this is known as circular polarisation.
The whole of the transmitting medium participates in all of the above waves.
But it is perfectly possible for only part of a medium (usually the surface) to participate - These are of course surface waves.
Now as Oke has mentioned there are two principal modes of action by the particles of the medium. Which one occurs or can occur depends upon the medium itself.
The two modes correspond to transverse and normal forces (stresses) in mechanics or if you like shear and tension/compression.
Now a fluid cannot support shear in the body of the fluid, only at the surface, so can only transmit normal or pressure waves, such as sound.
As we note from the ocean it can support transverse or shear waves at its surface.
Solids, on the other hand, can support both types through the body and at the surface. Surface Acoutic wave devices for instance are surface pressure waves.
Electromagnetic waves are transverse waves. I suspect some of the surface waves you are asking about are 'guided waves'. A guided wave propagates within a guiding 'channel' which provides physical boundaries that reflect the wave energy beckwards and forwards between them, keeping the wave inside the channel.
Some frequencies of radio work like this. A normal radio wave propagates out in all directions, but certain frequencies are reflected from the ionosphere, back to the ground, where they are reflected back up again and so on.
In this case the direct transverse electromagnetic wave is called the surface wave and the reflected wave the sky wave.
Electromagnetic waves can also be polarised. Hence the lateral waves you were asking about, these are polarised transverse waves. Naturally antennae have to be correctly oriented to sync with the polarisation.
Hope this all helps.