Are some CPUs implemented in standard cells and are others customized?
No, analog IC designers were not creating microprocessors under the direction of digital architects. It's more correct to say that digital integrated circuit designers needed to know quite a bit about how the transistors actually behaved.
The choice of whether a particular part of a digital IC will be crafted using standard cells or hand-drawn circuits is simply a matter of economics. For dense, highly-repetitive structures like memories (cache, microcode ROM, register file) it made sense to invest time in handcrafting the few basic cells that would be tiled together...the result was much smaller and faster than an equivalent circuit made from standard cells.
Blocks of "random logic" such as state machines and small counters were created using standard cells and CAD tools. Creating hand-crafted layouts for these blocks would have taken an enormous amount of time and provided little benefit. Instead, people worked to make the CAD tools and cell libraries better.
The "fuzzy" appearance you're seeing in the first microphotograph is indeed the result of an automatic place-and-route algorithm synthesizing a design using a standard cell library.
Older parts, like the AMD386 in the second image, predate the existence of these algorithms. The entire design was painstakingly placed and routed by hand, accounting for its more orderly appearance. (On the other hand, the lack of a single process producing the layout accounts for the large areas of interconnects required on the 386 -- a PAR algorithm probably could have produced a much more efficient layout.)
Note that this doesn't mean that there's anything analog about the AMD386. It's an entirely digital part! Analog components in modern chip designs often look more "orderly" because they contain physically large parts which must be spaced apart from other logic, like the circular inductors in the lower right of the nRF51822.