Correlation between a/c position and map

(I searched and couldn't find anything relevant.) What determines the position of aircraft relative to the map (or the map relative to the aircraft, if you like)? Yesterday at both Larnaca (LCA) and Bristol (BRS), aircraft were apparently taking off and landing well south of the runway (a couple of km), although other airports I checked were OK. Today they are both spot on, with aircraft going down the runway centre line.

I'd be interested in knowing what determines the relative positioning, and what can cause it to go wrong.

(Both the web page and the Android app are/were behaving identically.)