Classification of swords is not “an exact science” and there are overlaps which makes it complex. We will cover here a few but it is important to point out that some of these classifications are modern constructs and not terminologies used in the time when these swords were used.
Great sword is a type of sword that had length between 90 cm and 120 cm. They were design to be used with one or two hands but their grip may be designed specifically for one hand, two hands or the “hand-and-half” grip (which could easily be used with one hand but had place for a second hand for a more powerful blow).
Long swords of Middle Ages and Renaissance fit into this group as well as Scottish claymores.
Bastard sword is a “hand-and-half sword”.
Long knife class have blade from 30cm to 60cm and are considered swords. They have no cross guard or have a very short one. Seax used by Germanic peoples of the Migration period, gladius that was a sword of Ancient Roman foot soldiers, and xiphos used by Ancient Greeks belong in this class.
Bidenhänder or zweihänder is a two handed sword that could be used with only two hands (not like smaller variants that could also be used with one hand). They had up to 180 cm in length and had weight from 2 to 3.2kg.
Edgeless swords: type of swords that are designed for thrusting and not for cutting. Panzerstecher was used in Germany and in the East Europe. It had a cruciform hilt with a grip for two hands and a sharp point. It was designed for fighting against mail or plate armor. Its length ranged from 0.9m to 1.6m. Tuck, estoc and verdun were variants of panzerstecher. Small sword, smallsword or court sword evolved out of the rapier of the late Renaissance. It had blade with triangular cross-section and a sharp point.
Hangers and sabers is a class of single-edged, usually curved bladed swords. Hanger (also known as wood-knife, hunting sword or cutlass) is a long knife or a short, broad saber or slashing sword. It hangs from the belt, hence the name. It was used as a tool in a hunt and as a weapon of war. Falchion had a curved blade but a straight edge and was used in Europe from 11th to 16th century. Saber was a curved blade sword used in cavalry. Scimitar is a type of saber used by the Turks or Ottomans and Persians.
One more type of classification of swords is a modern classification called Oakeshott typology created by historian and illustrator Ewart Oakeshott. It is a narrower classification used to categorize the swords of the European Middle Ages from 11th to 15th century. It has 13 main types labeled from X to XXII and few subtypes marked with a, b, c... All types are divided into two groups: Group I and Group II where Group I (Types X-XIV) consists of swords which were used to fight against an opponent in a mail while Group II (Types XV-XXII) has swords designed to against a foe that has plate armor on.