PCI audio card is computer sound device installed inside of case. There are kinds of the internal sound cards:
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PCIe, PCI, ISA is a data buses. It is sorted by throughput descending (left to right).
Data bus is a set of wires passes information from sound card to/from central processor unit and memory of computer. Usually on motherboard there are some sockets PCI and/or PCIe.
ISA bus already has sunk into the past.
Do whether PCIe gives something (compared with PCI)? Nothing for productivity of sound system.
PCI bus has quite sound stream throughput up to 352.8 kHz/24 bit/7 channels and more. Simply PCIe is more modern bus type.
PCIe appearing for improve performance of video cards. Unlike PCI sockets, PCIe have less contacts. It increases their reliability. New motherboards has number of PCIe slots more and more. But PCI slots less and less.
Therefore manufacturers of computer accessories reduce number of PCI sockets on mother boards. Probably PCI sockets will disappear at some years.
Usually PCI or PCIe sound cards outlive several computers where installed. Therefore it is better to take PCIe card on prospect. Though the choice of professional PCI sound cards is more.
There is a popular prejudice: builtin sound cards considerably are subject to interferences inside of computer case. PCI sound card catches interferences "by air". Notice, these interferences catches sensitive input circuits of audio cards not only "by air". Also electric impulses pass on power feed. This type of interferences suppresses by power line filters.
Design (shielding, lines of board, etc.) the modern professional PCI sound cards allows to get rid to "air" interferences. Electric filters allows to struggle with interferences in power supply circuits very effectively.
Therefore no difference by noise level of builtin and external sound cards.
Some PCI audio cards have an external modules with professional sockets, ADC and DAC (analog-digital and digital-analog converters). Creative X-Fi top configurations have into external module more high-qualitative ADC/DAC, than PCI module installed on motherboard.
External modules of professional cards allows to connect more convenient big connectors (TRS, XRL) used in the studio equipment.
Modern builtin (onboard, integrated) sound chips is high-quality playback device.
The chip inseparable placed on motherboard of computer.
If you use digital outputs only with external hi-fi AV-receiver, quality of sound will not disappoint you.
On-board sound card has:
1) Low quality of record;
2) Absence of "native" ASIO-drivers for solving next problems:
- significant time delay of a sound at real-time when using audio plugins at DAW (Cubase);
- fixed sample frequency playback, resampling in real time. Resampling quality in this case in doubt;
3) Absence of balancing inputs and outputs.
About external sound card here...