The set of components is an absolutely individually topic. This overview should just show different ways of how to categorize your components. Please always have a look on your individual setup and use this overview only as an inspiration.

Further readings

The component gallery

Checklist of core components

Design System Checklist

The component series

The anatomy of a button - UI component series

Text fields & Forms design - UI components series

Selection controls - UI component series

Set of core components

Carbon

— Source (Carbon Design System)

Atlassian

avatar
avatar group
badge
banner
breadcrumbs
button
checkbox
code
dropdown menu
flag
inline dialog
inline message
logo
lozenge
modal dialog
pagination
progress indicator
progress tracker
radio
section message
sleect
spinner
tabs
tag
text field
toggle
tooltip

— Source (Atlassian)

Material design

app bars: bottom
app bars: top
backdrop
banners
bottom navigation
buttons
buttons: floating action button
cards
chips
data tables
date pickers
dialogs
dividers
image lists
lists
menus
navigation drawer
navigation rail
progress indicators
selection control: checkboxes
selection control: radio buttons
selection control: switches
sheets: bottom
sheets: side
sliders
snackbars
tabs
text fields
tooltips
time pickers

— Source (Material Design)

Shopify

account connection
action list
button
button group
drop zone
setting toggle
app provider
callout card
card
empty state
frame
layout
media card
page
page actions
stack