I believe they are talking about the same Person, but believe many grave errors about Him. When the Pharisees in Christ’s time spoke of Jesus, for example, they were talking about the same person Peter was–they weren’t talking about some other person–even though Peter rightly believed He was the Christ, the Son of the Living God, while many Jews did not (as Muslims do not).
This is just common sense. For another example two different historians may assert different conceptions of the same figure. Some say George Washingon was a virtuous and honorable man his whole life, etc. Others say he wasn’t so great, he practiced scalping and other war crimes, etc. The two historians are still talking about the same person, but with vastly different understandings of him (and where they conflicted, at most one could be correct, the other would be in error).
This is also different than the sense in which Christ says we must believe in Him. This does not refer to just believing He exists, but rather believing His doctrine, His promises, etc.