Do "compiler" and "assembler" correspond to frontend and backend phases of a compiler?
Some compilers translate source code to assembler code in one or more phases, then use an assembler which will produce bit patterns of the instructions needed, and store them in a file that the linker understands. 

Many compilers don’t do this. Producing code in assembler (human readable) form takes time. Parsing the human readable form, which is the first thing the assembler has to do, takes time again. Substantial time, actually. By generating the output directly that the linker needs, substantial time can be saved. 

So usually there is no assembler involved. 

And please note that (1) all these charts are just examples of how you could. The UCSD Pascal compiler had one single phase for compiling. And (2) gcc is more than a compiler. There is no iron rule how a compiler has to be organized. It's just a program, and the developers of that program figure out a good way to make the software work. 

PS. Do “compiler” and “assembler” in Figure 1.5 and in the GCC figure respectively correspond to frontend and backend phases of a compiler in Figure 1.6? Absolutely not. The whole Figure 1.6 is just a more detailed view of the "Compiler" box in Figure 1.5.