'Nucleic acid circuits'/'DNA circuits' are conceptually entirely different to 'genetic circuits'.
In the former, you design sequences of DNA such that complementary base pairing means they can displace each other in cleaver ways. This lets you create some interesting things, like oscillators [1], amongst others [2]. These do not need any of the apparatus of the cell to function, so work in solution; indeed, if they were inside cells they would get digested by nucleases. The thermodynamics of DNA/RNA folding is fairly well understood, and the range of structures in much more limited than that of proteins. A major drawback of these circuits is that they function very slowly.
By 'genetic circuits', people usually mean a genetic regulatory network [3] - essentially you combine existing genes in new ways, by chaing the regulatory sequences before each gene. For example, you can construct an oscillator from three genes by having the first repress the second, which represses the third, which represses the first [4]. Here you aren't designing new proteins (which is extremely hard), but rather modifying existing ones. Since these circuits require producing new proteins from DNA, they require RNA polymerase, the proteosome, ATP, the necessary monomers etc. so can only function inside a cell (or cell-free expression system containing these components).
In the former, you design sequences of DNA such that complementary base pairing means they can displace each other in cleaver ways. This lets you create some interesting things, like oscillators [1], amongst others [2]. These do not need any of the apparatus of the cell to function, so work in solution; indeed, if they were inside cells they would get digested by nucleases. The thermodynamics of DNA/RNA folding is fairly well understood, and the range of structures in much more limited than that of proteins. A major drawback of these circuits is that they function very slowly.
By 'genetic circuits', people usually mean a genetic regulatory network [3] - essentially you combine existing genes in new ways, by chaing the regulatory sequences before each gene. For example, you can construct an oscillator from three genes by having the first repress the second, which represses the third, which represses the first [4]. Here you aren't designing new proteins (which is extremely hard), but rather modifying existing ones. Since these circuits require producing new proteins from DNA, they require RNA polymerase, the proteosome, ATP, the necessary monomers etc. so can only function inside a cell (or cell-free expression system containing these components).
[1]: https://www.researchgate.net/publication/50304896_Programmin...
[2]: http://research.microsoft.com/en-us/projects/dna/
[3]: https://en.wikipedia.org/wiki/Gene_regulatory_network
[4]: https://en.wikipedia.org/wiki/Repressilator