Without getting into the history of red and blue tape, the standard work flow is that the schematic software exports a Netlist. This is a pseudo-standard file format that contains the parts, their pinouts, the signal names (each signal from here to there is called a net; hence, netlist) and the from-to connections. The netlist is imported into a layout program. That program looks in its library for the parts, and puts them up on the screen with everything connected by simple straight lines. This is called the rats nest display. Then you drag the parts around to place them and turn the connections into pc board traces using the drawing tools in the program. In this way, anything connected on the schematic is connected on the board; nothing is lost in a manual translation from one environment to the other. This is why everyone on these fora are so hyper about the schematic - it is the anchor for everything about the design. Pro schematic packages let you define minimum trace widths for power runs, ground planes, matched lengths and impedances, and other things usually left to the layout stage *in the schematic*. In a workplace where the schematic designer and board layout person are different people, this is how they communicate in a way that does not require a stack of cocktail napkins. Everything is "flowed down" from the schematic, making it the primary control document.
Newer programs integrate the stages, so an all-in-one program doesn't export/import a netlist to itself. A critical part of this process is the libraries. Particularly if you are using separate programs for the schematic and the pcb, the library device names much match or one program will not be able to interpret the netlist from the other.
And, physically prototyping a circuit on perf board is not a mandatory step in translating it to a pc board design. Educational, prudent, conservative, and possibly cost effective, maybe; "the first thing"? - not in an age of proto boards and decent simulators.
ak