Rieder et al. (1988) considered this name to be synonymous withillite. They use the name illite vaguely, as a compositional space for any interlayer-deficientdioctahedral mica. However, they also suggested that all hydromicas (=interlayer-deficient micas) could be considered to be mixed layer structure minerals, and thus illite may be an interlayered mica and smectite.
The name hydromuscovite is typically used to refer to fine grained, often pale green, interlayer deficientmuscovite (i.e. potassium deficient), but the literature is full of inappropriately named examples. Hydromuscovite probably does not exactly equal “illite" in all cases; some may be just fine grained muscovite and some may be mixed layer phyllosilicates.