A point in time is often represented as Unix Time, or as a human-readable ISO 8601 date in UTC time string.
For example:
Seconds since Epoch, or Unix timestamp, in seconds or milliseconds:
1529325705
1529325705000
2018-06-18T15:41:45+00:00
Is there a one-to-one and onto relationship between the two? In other words, is there a point in time with a single representation in one format, and more than one, or zero, representations in the other?
Yes, it is possible to find such a date. From the wiki article on Unix time:
Every day is treated as if it contains exactly 86400 seconds,[2] so leap seconds are not applied to seconds since the Epoch.
That means that the leap seconds themselves cannot be represented in Unix time.
For example, the latest leap second occurred at the end of 2016, so 2016-12-31T23:59:60+00:00 is a valid ISO 8601 time stamp. However, the Unix time stamp for the second before, at 23:59:59, is represented as 1483228799 and the second after, 00:00:00 (on January 1 2017) is 1483228800, so there is no Unix timestamp that represents the leap second.
In practice, this is probably not a problem for you; there has only been 27 leap seconds since they were introduced in 1972.
It might be worthwhile to mention that most software implementations of ISO 8601 does not take leap seconds into account either, but will do something else if asked to parse "2016-12-31T23:59:60+00:00". The System.DateTime class in .NET throws an exception, while it's also conceivable that a library would return 2017-01-01 00:00:00.