POP3 and IMAP are two distinct protocols. The UIDs used by these two protocols are not related and are not supposed to be the same at all. In fact, a POP3 UID is an arbitrary string while an IMAP UID is a 32-bit number (transmitted as string).
In theory, it is possible to write a mailserver that supports both IMAP and POP3 use the same UID for both protocols, but I'm not aware of any server that would actually do this. In practice, you have to treat POP3 UIDs and IMAP UIDs as unrelated values.
RFC 1939 (POP3):
The unique-id of a message is an arbitrary server-determined string, consisting of one to 70 characters in the range 0x21 to 0x7E, which uniquely identifies a message within a maildrop and which persists across sessions.
RFC 3501 (IMAP):
(Unique Identifier (UID) Message Attribute is) a 32-bit value assigned to each message, which when used with the unique identifier validity value (see below) forms a 64-bit value that MUST NOT refer to any other message in the mailbox or any subsequent mailbox with the same name forever.