People who do not work across disciplines can sometimes be confused about various categories of evidence and how they are used to reconstruct the past.
Historical evidence is written evidence about the past.
Archaeological evidence is material evidence about the past.
These categories of evidence are not necessarily mutually exclusive. An inscription found in situ (in place) on an archaeological dig is both archaeological evidence and historical evidence.
We attempt to reconstruct the past from various types of evidence. Generally, historians have no training in or competence with archaeological evidence, and archaeologists generally have no training in or competence with historical evidence. There are some very notable exceptions to those generalizations; a number of scholars successfully work with both types of evidence and certain disciplines routinely work with both types of evidence.
Archaeological evidence and historical evidence provide different pictures about what happened in the past. These viewpoints might be complementary or contradictory. In both cases we can only deal with the evidence we have.
For example, the inscriptions from Til Barsip (modern Tell Ahmar) indicate that the dynastic succession at Masuwari was complicated; they do not, however, give us the names of all the rulers involved. So we can only work with inadequate evidence.
To show how the archaeological and historical record give different pictures, consider Nicaea. From historical sources we know that Nicaea was near Constantine's summer residence. We have no archaeological evidence that he was ever there or ever paid any attention to the place. The lack of archaeological evidence does not prove Constantine was never there. On the other hand archaeological evidence tells us that the theater seated 15,000. I know of no historical evidence that provides us that information. The lack of historical evidence does not mean there was no theater.
Sometimes historical and archaeological evidence overlap. Sometimes they conflict. Most of the time they do neither. Each provides its own sort of evidence. One cannot just expect the two types of evidence to corroborate each other. Much of the material in the Bible, for example, is not and cannot be corroborated archaeologically. There are points at which the archaeological record does corroborate the Bible. But archaeology does not necessarily corroborate every point one might like.
Historians not used to dealing with archaeology have a tendency to overestimate the extent to which the archaeological evidence can be expected to corroborate the historical evidence.
Historians not used to dealing with archaeology have a tendency to overestimate the extent to which the archaeological evidence can be expected to corroborate the historical evidence.