The concept of daisho, literally “big (and) small”, was simple: a sword paired with a sidearm that can be used when the other was not suitable. The vast majority of samurai would wear a typical long sword alongside a shorter one for use at closer range, such as indoors, or in the battlefield if the spear and sword were lost or otherwise not useful for engaging the enemy.
The origins of daisho was around the Momoyama period, the final portion of the Sengoku era, a time of warlordism in Japan during the 1500–1600s. But in reality samurai had always worn a backup weapon on their person both in battle and in plain clothes, centuries before the term came into being.
Technically, daisho specifically refers to katana and wakizashi, but some more specific points:
-in earlier periods there was no such thing as a katana, it was itself a straighter variant of the tachi, a sword that was suspended from the belt and drawn and used as a cavalryman’s blade- the samurai were originally mounted horse archers.
-wakizashi in modern terms refers to a shorter blade than the katana but otherwise constructed and designed just like one; but in its broadest sense wakizashi is itself a portmaneau of “Waki” and “Zashi”, Secondary and Insert, respectively. So daisho worn by samurai could and often were just any two blades of any length- it was just more practical to have a shorter blade on hand.
-daisho therefore could be referred to ANY pair of blades and the specific lengths and types did not matter: a samurai could wear a tachi with a tanto, a katana with a tanto, wakizashi with tanto, or even just two katanas.
-another fun fact, although tachi and katana had design differences, the other difference was simply the way it was worn, tachi were hung with a suspended scabbard, whereas katana scabbards were inserted into the belt sash. Samurai deployed as cavalry with only katana would simply have used a suspended scabbard.
The image of a samurai wearing matching pairs of swords is a matter of fashion, so daisho does not require matching pairs. Unlike richer samurai such as daimyo warlords that could afford swords that double as works of art, poorer samurai may not have purchased a matching set, or had different sets passed down from generations, or were collected from dead bodies after a battle. It is a popular image, but not necessarily the most prevalent one in reality.