There are a few explanations worth considering before drawing any conclusions.
The most common reason for a name match with different details is that it is simply a different person. Common names produce multiple results across inmate databases, and without a unique identifier like an inmate number it is easy to pull up someone who shares a name but is an entirely different individual. That is the first thing to rule out.
If you are confident it is the same person, a facility discrepancy usually means one of two things. Either the data on one of the sites has not been updated recently, or he was transferred after the information was pulled and the new location has not propagated across all databases yet. Inmate locator sites pull from state and federal records but they do not all update at the same frequency. Some lag by days, others by weeks.
The age discrepancy is harder to explain away and worth paying attention to. Facility databases pull age and date of birth directly from official records, which are generally accurate. If the age is significantly different between two sources showing the same name, it is more likely two different people than a data error.
The cleanest way to resolve this is to ask the person you have been corresponding with directly for their inmate number and facility name. That combination is unique to one individual and removes all ambiguity. If they are who they say they are, confirming those details should be straightforward.