Both shows have a similar starting point in terms of plot: FL is older, married and an experienced manager in showbiz who picks the ML and guides them into becoming a star. Bijo to Danshi is about the hard work and challenges involved in this journey and how the FL manages her personal life alongside all of it. There is also a hint of romance, but it's not the main plot.
Similar in the sense that the fictional world has rules which the FL struggles against. FLs in both shows are strong, resourceful characters who know what they want and fight against their "fate".