In general, PCB is a term used for rigid PCB. In case we have to mention Flexi PCB, we use term as Flexi-PCB. Though this is a term there, but flexible PCB are not totally flexible. This name is little contradictory as boards are not really flexible. The market of flexible pcb have so grown that there are companies dedicatedly working upon flexible PCB manufacturing and assembly only. Flexible circuits are obviously unique among electronic packaging technologies in that they o er a wide variety of advantages unobtainable using conventional rigid interconnection technologies. Freeform integration of electronic elements through all three dimensions of space is highly liberating to the design process.

flexible PCB
A interconnection on the circuit trace is similar to circuit trace on rigid circuit. there can be considerable differences between designing a rigid PCB and a flexible PCB. Because of the flexibility feature, there are unique issues affecting robustness. For example, since flex can bend, one needs to be sure that bending does not crack or break solders joints near a bend location. For this reason, design features like radiuses corners and filleted pads are common on flexible circuits. Another issue is that the substrate used for flex is not as dimensionally stable vs. its rigid cousin. Allowances for dimensional changes may be required for Flexi PCB designs. Most PCB design software is tailored to rigid printed circuit materials and features. Tradeoffs occur when this same software is used to design flexible PCBs.
rigid PCB
Rigid PCBs and flexible PCBs have very similar fabrication steps and often use the same equipment and equipment manufacturers. For example, photo imaging the base circuitry layer can use virtually identical technology. The differences arise because of the difference between handling a rigid board versus a flexible substrate. Some ultra-thin circuits are extremely flimsy and need special material handling systems. While a PCB is relatively easy to handle, a thin flexible circuit may need special clamping, fixturing or vacuum systems to hold it in place while processing. Some very high-volume flexible PCB manufacturers process circuits in a continuous reel (reel-to-reel). Reel to reel processing uses significantly different material handling mechanisms vs. systems processing discrete panel sizes.
Flexible circuit boards provide unlimited configuration opportunities that often results in very odd shapes and sizes.

Circuit boards often are rectangular or may have some notches or curved outlines routed. Because of this nuance, steel rule dies and hard tool dies are probably used more often for flexible PCBs than for boards, at least for ultra-high-volume applications. Laser definition of the circuit outline is also a common flex circuit process. Other differences in tooling involve fixturing that may be required to handle flexible substrates.
Flexible PCBs require different dielectric materials such as flexible photo-imagable solder mask or laminated cover lay. he most common flexible dielectric is laminated film dielectric bonded to the substrate with high temperature and pressure, a solution rarely used for rigid PCBs.
Flexible PCBs constitute about 10–15% of all PCBs produce globally, so there are far more applications that use hardboards than flex. The biggest advantage for flex is that it can reduce the size, weight and amount of hardware used for many electronic packages.
If you have an application that requires multiple planes of interconnections, or there are active bending or flexing requirements for parts of the package, then a flexible PCB may be your best choice.