A catalogue is just that what one would understand usually: it's a table of stars with their coordinates and possibly other properties like relative or absolute brightness, proper motion etc. The accuracy depends on how it was created, thus mostly is expression of the available instrumentation, processing pipeline and its limitations. They usually are output of a particular mission or survey and represent the observations in tabular format and help to make sure different people talk about the same thing. Often the stars in a catalogue are thus also assigned a number to make it easy to refer to.
The most recent star catalogues are those from the Gaia mission, the older yet still often used catalogues are like Hubble Guide Star Catalogue which hold MUCH fewer stars, but the brighter ones only. There's also specialized ones which focus on particular type of stars like the General Catalogue on Variable Stars - but all those are only a selection.
Star maps and planetarium software need catalogues as input - they simple read the table and then display it somewhat differently. Both need to know where to place stars. As such their accuracy depends for one on the accuracy of the catalogue(s) they use - and on the accuracy of their projection which is at least limited by the point or pixel resolution but also the need to draw stars with more than one dot or pixel, especially to also indicate different brightnesses.