Traffic Alert and Collision Avoidance System (TCAS) is an implementation of the ICAO Airborne Collision Avoidance System (ACAS) standard. In fact, it’s currently the only implementation of the ACAS so the two terms, TCAS and ACAS, are often used interchangeably. TCAS gives Traffic Information about other ‘cooperating’ aircraft which are displayed as various symbols in various colours (depending on system parameters), and will also tell you how to get out of the way - as long as the other aircraft is ‘cooperating’.
Traffic Advisory/Alerting System (TAS) is a broad definition that covers all the other systems which tell you where some of the traffic is, but won’t tell you how to get out the way; TAS use a variety of data to generate traffic information and warnings or alerts. The obvious data source is SSR information, but systems also typically use GPS in conjunction.
A locally-produced UKAB TCAS II version 7.1 interactive TA/RA reckoner tool can be downloaded. To use the tool, enter the reference aircraft 'Airliner' and interloper aircraft 'Fast-jet' KTASs in their respective yellow cells and then select the height of the encounter. Enter a closing angle if desired to display the relative bearing on the chart. The first 2 charts show a selection of TA and RA ranges for various heights, whilst the 3rd chart shows the TA and RA ranges at the selected height. The TA and RA ranges for the selected closing angle are displayed in the grey box.
Other useful information on TCAS/TAS can be found at the links below: