～の時 vs ～歳の時: What's the difference?

Question

When referring to a time where one was a certain age, are there any differences in meaning, nuance or usage between saying, for example, 18の時 and 18歳の時.

I always thought you needed to have the 歳, but I ran into an example of it without it, so now I'm wondering.

Bonus question: Is this different for はたち? I.e. can you say 20の時?

Answer 1

The nuances are pretty much aligned with the English equivalents

When I was 18, ...

When I was 18 years old, ...

Appending 歳 is more complete and would be favoured in formal situations (e.g. as part of 丁寧語).

Bonus question: 20のとき sounds childish (albeit you being clearly over 20), like [5日]{ごにち} instead of いつか, so はたちの時 escapes the simplification rule and would be preferred in both formal and informal contexts.