I am reading about the algorithms to convert from  date and time format to Julian Date from the Fundamentals of Astrodynamics and Applications by Vallado (4th Edition) p183.

My question is specifically regarding the differences in converting UT1 vs UTC to JD(UT1) and JD(UTC) respectively. The formula provided has term which needs to be changed depending on if the day contains a leap second or not. Would I be correct in thinking that UT1 => JD(UT1) requires no accounting for leap seconds in contrast to UTC which does? I guess my confusion is arising from the language in some literature I have read referring to both UTC and UT1 as "non-uniform" time systems. I understand UTC is discontinuous due to insertion of leap seconds and suppose that UT1 is continuous but non-uniform in the sense that the definition of a second is not constant.

Just wanted to get some confirmation/clarification.

Thanks.