I just got confused. I thought that for a 380 it is a 355 bullet, but I read that 380 or 9mm is now 356. I want to start to reload these and don't want to order the wrong size.

9mm is .355
38 super is .356.

The .356 can be hard to find, so I always shot .357 bullets in my .38 super. I never had any issues doing so, but I had a modern strong design.

Your barrel will vary more than 0.001 in.

Raven some of the size difference will also be in bullet construction. A 9mm bullet is .355 ish, if you get a cast or plated bullet (Rainier, for example)the bullet may be sized larger. A jacket bullet doesn't compress as easy and may be made smaller. You may also find custom cast bullets in two or three different sizes for competition bullets like those used for bullseye pistol.

The thousandth of an inch isn't a factor unless you are at either end of the load range. Too light and the bullet sticks or too heavy and give a little extra pressure.

RAVEN... you'll find even factory bullets marked .356" on the label may only measure .355" or .3555" or conversely bullets marked .355" might be .3555" or even .356"
Generally, cast bullets for any given caliber are one-thousandth oversize versus the jacketed fodder.
That 0.001" variation even among jacketed bullets shouldn't be an issue, but definitely don't use the something like the 9mm Makarov (9x18mm) which uses a nominal bullet diameter of .364/5" in your 380 Auto brass.