A spear is a shaft with a sharp object on the end. A lance is sharp at the end but gets wider as it gets closer to the weilder. So flan's "lance" is shaped like a spear.
Spear = General class of weaponry characterized by having a an extended haft with a bladed point.
Lance = Cavalry spear, intended to be used from horseback. Some versions have a conical shape others have a more typical spear shape.
Javelin = Throwing spear, designed for distance and accuracy when thrown. They are light weight and as to be carried en masse, they are a projectile weapon.
Flandre's weapon is... odd. In fanart I've seen, it's mostly depicted like a Yari in it's usage (Japanese two-handed spear that is to be used in hand-to-hand combat only).
Flandre's Second Spell Card (Taboo "Lävatein" or Lævateinn) has the same name as the sword (wand in some versions) of Loki, a Norse god known for causing mischief. This sword/wand is used by the fire giant Surt in Ragnarok (the Norse equivalent of the Apocalypse) to burn down the whole world, except for one safe haven. Fitting that Flandre would be wielding a tool of such destructive might.