A default route is the route that will be used isif there's no other route that matchmatches the destination in the routerrouter's forwarding table.
aA full routing table is a table which contain all the routes the BGP neighbor is aware offof.
aA partial table is a table filtered (with route map, community...) so that only some specific routes are exchanged.
If you are connected to the Internet through a single ISP, a default route is enough, since there's only one possible path, so there's no point in having 500 000,000 routes in memory that all pointspoint to the same next-hop.
If you are connected through several ISPISPs with BGP and want to always use the "best" path, then a full routing table makemakes sense. In this case the default route will (almost) never be used since the router knows every possible destination with a specific route.
However a full routing table take some memory and also more CPU power (and time) to perform thea lookup for each destination among the 500 000,000 known routes.
When athe vast majority of your traffic will take onone path and only some specific destinationdestinations will take another path, a partial table is more efficient.