The evolutionary path is gladius -> spatha -> Migration Period sword -> Carolingian sword (which is more commonly called the "Viking sword", but "Carolingian sword" has plenty to recommend it as a better name).

But they aren't that similar in design. The Carolingian sword is about 50% heavier, has a blade about 50% longer, the blade has a broad fuller and a rounded tip which the gladius usually has a diamond-section or lenticular-section blade with a pointy tip. The Carolingian sword has a metal guard and pommel, while the gladius usually has an organic guard and pommel.

Over the evolutionary path above, the various features change one by one, so the transformation from gladius to Carolingian sword was gradual rather than sudden, but the final difference from start to finish was large. Beyond both being one-handed double-edged swords, there isn't much similarity.

The evolutionary path in pictures:

• Gladius (replica): https://commons.wikimedia.org/wiki/File:Uncrossed_gladius.jpg

• Spatha (replica): https://commons.wikimedia.org/wiki/File:The_Decurio_02.jpg - similar hilt, but much longer blade, multiple fullers, more rounded tip, weight intermediate between gladius and Carolingian sword

• Migration Period sword (original hilt): https://commons.wikimedia.org/wiki/File:Ringknaufschwert_1.JPG - hilt of mixed organic and metal parts (the organic parts are long gone in this example, and the metal parts remain; the space between the metal plates in guard and pommel show where the organic parts originally were)

• Migration Period sword (replica): http://www.deltin.it/2071.htm - a replica of a sword of the type above, showing what it might have originally looked like. Heavier and longer than the spatha.

• Carolingian sword (original): https://commons.wikimedia.org/wiki/File:Double-edged_sword_from_a_grave_in_Birka.jpg

Since the Carolingian sword is substantially different in design from the gladius, and is much more optimised for cutting (as opposed to the cut-and-thrust gladius), the usage would be quite different. In common with the gladius, it would be used with a large shield (of different design from the shield used with a gladius), but the same could be said for very many one-handed swords of various designs. Other short swords such as the Greek xiphos and the Chinese Warring States bronze jian might have had a lot more in common with the gladius in the ways that they were used, despite lacking any close evolutionary relationship - form fits functions.