Is Fresnel diffraction really visible if slit width is similar to distance from screen or does diffraction disappear in that case? Diffraction phenomena occur when, named $a$ the amplitude of a slit and $\lambda$ the wavelenght, $a \sim \lambda$ or even $a<\lambda$ (full illuminated screen).
Therefore if $a\gg\lambda$ diffraction phenomena are not visible.
On the other hand there are two types of diffraction: Frahunhofer diffraction and Fresnel diffraction.
In the first case the assumption is that, named $L$ the distance between the slit and the screen and $L'$ the distance between the source and the slit, $L'\gg a$ and $L\gg a$ (the wavefronts are planes).
Fresnel is the opposite case, in particular $L\sim a$. But initially I stated that diffraction phenomena are not visible if $a\gg \lambda$. Therefore, assuming (reasonably) that $L\gg \lambda$ how can Fresnel diffraction phenomena occur at all.
In other words, If I have $L \sim a$ or even $a>L$  but still $L\gg \lambda$ do I see diffraction (Fresnel diffraction) or do I just see one light spot (no diffraction)?
 A: You are taking 

there are two types of diffraction: Frahunofer diffraction and Fresnel diffraction

too literally. There is only one kind of diffraction physics: waves interfering with each other. The Fresnel and Frahunofer prescriptions are two approximation regimes for making the problem of computing results in closed form tractable.
You see the development of multiple approximation regimes in many (most? all?) fields where the completely general problem is infeasibly difficult (or even just annoyingly hard, actually). The near- and far-field approximations to electromagnetic radiation are close parallels to this case; but also Newtonian versus ultra-relativistic kinematics; the many, many approximation regimes of fluid dynamics; and so on.
It is often the case that this kind of approach ends with a intermediate regime where none of the approximations are valid that is poorly studied by comparison. I you have the right combination of mathematical skill and intuition there are papers to be had in those transition regimes.
