Is there a difference in meaning between "fill {something} in" and “fill {something} out” in American English?

The distinction between fill out and fill in is rather ambiguous.

Generally speaking, in the US, "fill out" means to "complete" the form -- supply all applicable information. "Fill in" means to put specific data in a specific place. Eg, "fill in your Social Security" number.

But, as I said, this distinction is not especially strong, and the context should be taken into account to hopefully either confirm or contradict this general assumption.

Yes, they both definitely mean that but one is American, the other one is British, however both are in use in AmE per my experience, as to the different aspect:

Fill something out per ODO:

North American

1 Add information to complete an official form or document.
‘he filled out the requisite forms’

Fill something in per ODO:

1.2 British Add information to complete something, typically a form or other official document.

‘he filled in all the forms’

And I agree with the AmE speaker who said they seem different in aspect. And I believe that difference in aspect comes from the adverbs in and out that are part of the two phrasal verbs.

fill + in

From Merriam-Websters in:

1 c : to or at an appropriate place

fill + out

From Merriam-Websters out:

3 b : to completion or satisfaction

3 c : to the full or a great extent or degree

Please also note comment below from @tchrist, where he points out the very good point that both AmE and BrE have their own idiomatic uses. In my answer I strictly intended to point out the difference between AmE and BrE in meaning "to complete a form", and the difference between the adverbs.