I was pretty curious about this as well and so I looked into this for a while. The best explanation I could come up with for the discrepancy in the numbers that you have is that over the course of a year, someone is relatively unlikely to kill themselves, but over the course of a lifetime the average person has a little over a 1% chance of killing themselves. Although this number is slightly misleading- as (if I remember correctly) the lifetime prevalence of completed suicide (worldwide) is probably closer to ~0.4% for women and somewhere over 1% for men.
It should also be noted that the suicide rate of an individual can vary wildly depending on their socioeconomic status, age, family stability, gender, educational attainment level, IQ, country of origin, number of disabilities/current health status, relationship status (divorced is a big one), religious affiliation (surprisingly predictive), presence of mental illness, and an uncountable number of additional life variables. On the low end, an individual with almost every single protective factor against suicide could easily have a predicted suicide rate of close to 0%, but an individual with a ridiculously unlucky life could have a predicted lifetime suicide rate easily over 80% (The groups with extremely high completion rates are considerably unluckier than what most people reading this would imagine).
The data surrounding suicide is kind of fuzzy because a lot of suicides aren't reported correctly and there hasn't been a ton of great analysis done on suicide in general. Most of the analysis I've found tends to have some sort of agenda behind it, and so it's difficult to find solid, raw data.
