Is there a difference? Are they actual terms? No, well maybe out there somewhere, but I just made them up.
What I mean by direct and indirect inspiration is, say, the difference between loving an artist and trying to have an element of your work similar to theirs (like lots of texture or an overall use of brown colour), and just doing your own work then realising it has characteristics in common with an artist. One is a deliberate attempt, one is when you say "oh I do that too!" after looking at their stuff for a while.
I often hear people say "I love such and such's work, why can't I do that?", or "I want to draw just like you!" and despite not really thinking that way myself (growing up I always just tried to draw what I saw realistically, and didn't know of anyone else who drew) I can understand people creatively finding themselves this way.
I think we all do both. Learning, we often do the former. It is inspiring our work on a directly influential channel. We are unsure of ourselves, we do not have the skills or knowledge of what's out there so need to lean on others. It starts to go into the territory of copying, but should not quite be. You may use different media, you may just want to see how they draw an eye because you can't get yours to look right. (P.S. never copy! Figure out your own way of doing it, as copying will never make it your work)
But I feel the second is more what happens to me at the point of creating. You surround yourselves with creativity in many forms, not just the work of other illustrators. For me, I love looking at travel photos or textiles. I can be inspired after looking at Pinterest for a while. I may not have any memory of what I looked at. It may be the next day and a certain warmth in the leaves I paint or an interesting pairing of hues appears in my work, or a certain size of a font interacting with the images that I wouldn't normally have thought of. Yet, looking back at those Pinterest images, you can't directly find what I have done. It is indirect, it is a subtle linkage of ideas in your head that makes something click for you. I love this feeling. I can be inspired by the minimal lines of a stone sculpture, or the harsh light against a fence in the morning, and this will inspire a strongly coloured flamingo card!
What do you think?