H323
H323 is an ITU-T umbrella standard released in 1996, which consists of signaling and transport and coding protocols. H323 is a multimedia conferencing standard and mainly used in professional video conferencing systems, but also used for pure VoIP applications. Part of the design is to specifically tackle the interconnection with PSTN by means of a gateway.
A simple set-up of H323 is depicted in the following figure (source: TERENA).

As seen in the figure the main components of a H323 system are:
• H323 terminals
• PSTN gateway for connectivity to PSTN
• Gatekeeper, which is the H323 IP telephony server
• MCU (Multipoint Control unit), which is a switch for establishing several node communication
SIP
SIP stands for Session Initiation Protocol. It is an application-layer control protocol that has been developed and designed within the IETF. The protocol has been designed with easy implementation, good scalability, and flexibility in mind. SIP was originally defined in RFC 2543.
Opposed to H323 which is an umbrella standard, the purpose of SIP is just to make the communication possible. The communication itself must be achieved by other means and protocols/standards. SIP has been designed in conformance with the Internet model. It is an end-to-end -oriented signalling protocol which means that all the logic is stored in end-devices (except routing of SIP messages).
Other standards
SIP and H323 are the dominant standards but also other signaling standards are available on the market. The important ones are MGCP and SCCP.
MGCP (Media gateway Control protocol) operates at the backbone of teh network and typically used by network elements like call agents which routes calls between gateways and media gateways. MGCP is documented in RFC2705.
SCCP (Skinny Client Control Protocol) is a proprietary protocol used by Cisco systems. It is a signaling protocol for Skinny clients, like Cisco hard phones and the Cisco call manager which connects the clients
Interoperability between SIP and H323
The interoperability between SIP and H323 can be established either by using proxies and gatekeepers which can handle both standards, or by using standard gateways depicted in the following figure