tabstop is how far the cursor moves when you press tab.
shiftwidth is how far text moves when you shift it with >> or <<
Normally you'd set them both to the same value so that indenting blocks of code with >> or << shifts them by the same amount as the tabstop.
There's also another setting 'shiftround' (which I only learnt about today in another comment) which makes shifts done with << and >> round themselves to the nearest multiple of shiftwidth.
never occurred to me to use >>. probably because the three keystroke savings didn't register with me. but that's what I mean, once I learn the basics, the rest are just gravy that don't stick in my memory.
Using < and > for shifts becomes even more powerful when combined with a movement, e.g. indenting 20 lines of code at once: 20>> or indenting an entire {} block (including braces) >a{ or an entire block (not including braces) >i{
> i've always used 0i\t\t\t\t...\esc to shift.
Also consider I instead of 0i (it's not quite identical, but should serve the same purpose).
It saves way more than 'three keystrokes' redenting a block though - you must do that every line - I typically visual select then > (or <), doing the whole lot in one stroke (excluding whatever variable amount to select, v} or similar often).
I only ever end up actually manually shifting code when I'm pasting python code from somewhere and it doesn't come in with the right indentation.
If I'm working in any other language it's == (for a single line), or = after marking a region in visual mode, or magg=G'a to just re-indent the whole file.
I haven't used vim as a daily driver in ~14 years; it's weird how the muscle memory of things like magg=G'a or gqip stay in your fingertips.
shiftwidth is how far text moves when you shift it with >> or <<
Normally you'd set them both to the same value so that indenting blocks of code with >> or << shifts them by the same amount as the tabstop.
There's also another setting 'shiftround' (which I only learnt about today in another comment) which makes shifts done with << and >> round themselves to the nearest multiple of shiftwidth.