where you could apply a tatoo to any skin instead of having to go and find a skin with a tatoo integrated into it?
That is done via LIE aka
Layered Image Editor in DAZ Studio. To access it go to the [Surfaces]-tab, pick for example the torso and click the texture (as if you would want to change it). "Layered Image Editor..." will be in the menu near the top.
The LIE combines the character-texture with layers (your transparent tattoo-texture that should match the UV-map of the characters) and pre-bakes temporary textures whenever a scene gets loaded or the layers change. I believe this is an optimization thing to prevent the GPU from loading a texture for a body-part AND the tattoo. So it's just one and that saves a ton of precious VRAM.
As far as I know Genesis 3 and 8 use the same UV-maps and therefore tattoo's for LIE can be used on both without problems.
Would they just end up being too stretched/distorted if it was done that way or something?
Yes, a tattoo on the belly for a thin characters placed on a fat biker would look stretched. It would stretch the same way as the torso texture due to the same UV-map.
Advanced custom tattoo:
It's possible to create a perfectly fitting tattoo with Blender's stencil painting feature. This works across model-seams and there is no stretching/distortion since you can basically 'spray' this on a custom body-part yourself.
Very over-simplified steps: Export the part(s) of your characters model from DAZ Studio with Subdivision level 0 to obj, load it Blender and set up materials, stencil paint into a new transparent texture, save it, load it in LIE.
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(The interface of blender changed obviously, but it still possible to follow this using common sense.)
related resources that helped me to figure this out in the past:
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I'd only recommend to try this for users that have worked with Blender before. It's not trivial.