Your understanding is correct. I think your textbook diagram is confusing, and partly wrong. I'll explain.
I think the dotted red line is supposed to represent a two source pattern with no superimposed diffraction effects. It is wrong because (1) it omits the central fringe (2) it makes the bright fringes too sharp. The intensity should follow a 'cos squared' graph, which is sinusoidal in shape. This implies that at mid-intensity (halfway up the vertical axis) the widths of bright and dark fringes should be equal. They don't seem to be.
The red solid line is the single slit diffraction pattern for a slit with a width of 2s, in which s is the distance between the slit centres used for the two slit graph. I find this confusing, because slits of this width couldn't have a separation s between their centres without merging into one wide slit. I suppose that the diagram makes no claim that the red dotted line and the red solid line should apply to the same set-up, but I'd rather they did.
The blue line is the single slit diffraction pattern for a slit with a width of (2/3)s. I've no quarrel with this: two slits of this width, with centres separated by s, would not merge, and could be used to produce Young's fringes, but there seems to be no graph which shows the 'modulation' of the Young's fringes by the diffraction 'envelope'.