Differences in Double slit experiment and 2 slit Diffraction

A realistic double-slit has two effects at play: there is single-slit diffraction from each sit (giving rise to the larger envelope) and there is interference between the two beams of light from each slit (giving rise to the smaller fringes).

Some sources take into account both effects, but some sources ignore the single-slit diffraction effects and simplify the slits as "point sources." Your first graph takes all effects into account, while the second graph only treats the slits as ideal point sources.

See my post here talking about this. I give a derivation for the point-source case (obtaining the equation for the second graph), and then at the end I give a derivation for the realistic case (obtaining the equation for the first graph).

They are the same thing. The broader envelope in the interference pattern is a result of the diffraction in each slit, while the more rapid oscillations result from the interference of waves from the two slits.

When the slit width is much smaller than the spacing of the slits, the envelope becomes so wide that it is essentially flat, so you get the second pattern, at least for small angles.

Sometimes (but not always) when people speak of double slit diffraction, the implication is that the slit width is comparable to slit spacing, so that the slowly-varying envelope is clearly evident in the interference pattern.