Hello Eark!

They mean the same thing, although there are certainly cases when one may be more appropriate than the other. Take for example:

Children under the age of 18 may not purchase alcohol (not less than the age of 18 . Stylistic)

Cleaning products are usually kept under the sink (not less than the sink - Physical location)

In most other situations they can be used interchangeably, with only very slight difference in meaning:

There were less than/under 500 people at the concert last night. (under sounds more formal to my ear...)

I can run 10 kilometres in less than/under an hour (under would be more usual, as I'm talking about personal achievement and giving a deadline of an hour)

It took me less than 3 years to build my house but I built my house in under 3 years (less than sounds more casual, with under we are relating our achievement with a goal.)

I hope this helps!