NOAA has a great guide on their website called A Pilot's Guide to Aviation Weather Services which covers these (and more)! They actually describe it better than I could.
The short version though is that TIBS is a telephone weather service while TWEB is a recorded route briefing that you can listen to while airborne. Both are used for supplemental information and don't replace an official briefing.
- TIBS Telephone Information Briefing Service
- TWEB Transcribed Weather Enroute Broadcast
- PATWAS Pilot's Automatic Telephone Weather Answering Service
TRANSCRIBED WEATHER BROADCASTs (TWEB) are continuous broadcasts of
recorded NOTAM and weather information prepared for a 50-nautical mile
wide zone along a route and for selected terminal areas. TWEBs are
broadcast over selected NDB and VOR facilities and generally contain a
weather synopsis, in-flight advisories, route and/or local vicinity
forecasts. Winds Aloft Forecasts, current weather reports, NOTAMs, and
special notices. TWEB outlets are listed below by state:
PILOT'S AUTOMATIC TELEPHONE WEATHER ANSWERING SERVICE (PATWAS), and
the TELEPHONE INFORMATION BRIEFING SERVICE (TIBS), provide continuous
recordings of weather and aeronautical information. The information
may include area and/or route briefings, airspace procedures, and
special announcements. Telephone numbers for PATWAS and TIBS locations
are found in the Airport/Facility Directory.
TWEBs, PATWAS, and TIBS are for preflight or inflight planning and
should not be considered a substitute for formal preflight briefings.