Wikipedia describes a tart as typically free-standing, with a firm pastry base, a thick filling and perpendicular sides, and a pie as having softer pastry, a looser filling and sloped sides that call for serving from the pie plate. The Cambridge Dictionary defines a tart as an open pastry case with a filling, usually of something sweet such as fruit. Familiar tarts include treacle tart, Bakewell tart, tarte Tatin and the savory quiche.
Medieval tarts were usually filled with meat. Over time sweet fillings of fruit and custard became the rule. The Italian crostata, an early open fruit tart, dates from at least the middle of the fifteenth century.
In French the single word tarte covers both pie and tart. The categories tart, flan and pie overlap without sharp lines between them.