Options, Settings, Properties, Configuration, Preferences — when and why?

Tricky, this, as there's no one single consistent style followed by all applications. As you say they are (broadly) synonyms.

In truth it doesn't really matter so long as your expected audience understands what you mean.

The biggest difference is between Properties, which usually affect a component or object, and the others, which affect the whole application.

Following an approximate lead from Visual Studio and other Microsoft products:

• Properties represent the characteristics of a single component or object in the application.
• Options alter global ways that the application works. Microsoft products use this to customise the UI toolbar, for example. There's an implication here that you can disable UI elements altogether (e.g. a "Simple" user interface or an "Advanced" user interface).
• Settings and Preferences change qualities of how the application works. The implication here is to change, not disable: for example, "Metric measurements" or "British Imperial measurements".
• Configuration is often where an application is customised for each user or group.

But there's no single rule.

I'd suggest you use Properties for object characteristics and Settings for everything else that's application-wide.

I just did a quick scan and wanted to post this list for reference.

Edge                        Settings
Google Chrome               Settings
Google Chrome DevTools      Settings > Preferences
Mozilla FireFox             Options (about:preferences) > Network Settings
Mozilla FireFox DevTools    Settings > Editor Preferences
Opera                       Settings

DeviantArt                  Settings
Facebook                    Settings, News Feed Preferences
GitHub                      Settings
Google                      Settings
IMDb                        Account Settings > Preferences
Instagram                   Options (aria-label)
JSFiddle                    Settings
StackOverflow               Settings > Preferences
Twitter                     Settings
YouTube                     Settings

FileZilla                   Edit > Settings
GitHub                      File > Options
Notepad++                   Settings > Preferences
VS Code                     Preferences > Settings

Audacity                    Preferences
IcoFx                       Options > Preferences > Options
Process Explorer            Options
TeamViewer                  Tools > Options
uTorrent                    Options > Preferences
Windows Media Player        Tools/Organize > Options

phpmyadmin                  Settings
XAMPP                       Config > Service and Port Settings
                                   > Log Options

MS Word                     File > Options > Proofing > AutoCorrect Options
                                                      > Writing Style Settings

Photoshop                   Edit > Color Settings
                            Edit > Preferences
                            Type > Language Options
                            3D > 3D Print Settings
                            Viev > 32-bit Preview Options
                            Window > Options

Windows                     Settings

Used as the parent (window/choice):

• Settings : 20 times
• Options : 10 times
• Preferences : 4 times
• Config(uration) : 1 time

Total mentions:

• Settings : 24
• Options : 15
• Preferences : 12
• Config(uration) : 1

Based on this, I'd sort these in this order (from general/fixed/app-related to specific/dynamic/user-related):

Settings > Options > Preferences

These aren't set anywhere, but I figured I might as well chip in my 2¢ on the topic. When I see these in an application, this is what they imply to me:

• Settings: "View or modify the list of things that can be set"
• Options: "We have set some things already, and give you the option to change them"
• Preferences: "Tell us how you prefer this to work"
• Properties: "Change one or more properties of this item"
• Edit: "This thing is already in a good state, but you can change it if you like"
• Configuration: "We have defaults, but they're so barebones you probably want to configure it yourself"

I think that one point of view is missing here namely the relation between configuration/settings/options/preferences.

To me a configuration or preferences contain many settings or options so there can be one setting or one option.

You usually say "Change this option/setting" and not "Change this preference/configuration", don't you?

When someone says preferences or configuration I understand it as a set of settings or options.