The intermediate fluctuation regime for wetting transitions is studied for (1+1)-dimensional systems. This regime is found to consist of three different subregimes resulting from the competition between the short-range part and the long-range part of the direct interaction between the interfaces. In subregime A, the short-range part is irrelevant, which leads to a wetting transition of infinite order. In subregime B, both parts are relevant and the critical behaviour is non-universal. In these two subregimes, all critical singularities can be expressed in terms of a single length scale. This scaling breaks down in subregime C for which the interfacial fluctuations are strongly non-Gaussian.