Why does `npm install` add / remove caret (^) to /

I have a project that I work on with two different laptops. Sometimes I add extra packages to my project, so I have to use npm install <package-name> (duh). When I do that, I git push up the new package.json and package-lock.json files, and when I switch computers I have to git pull those changes, then run npm install again to get that package onto the other computer.

I recently noticed and started caring that one laptop kept adding carets (^) to the beginning of every package version number. For example:

One computer set package version #s to look like this:

"regexpu-core": {
  "version": "1.0.0",
  "resolved": "https://registry.npmjs.org/regexpu-core/-/regexpu-core-1.0.0.tgz",
  "integrity": "sha1-hqdj9Y7k18L2sQLkdkBQ3n7ZDGs=",
  "requires": {
    "regenerate": "1.4.0",
    "regjsgen": "0.2.0",
    "regjsparser": "0.1.5"
  }
},

The other set package version #s to look like this:

"regexpu-core": {
  "version": "1.0.0",
  "resolved": "https://registry.npmjs.org/regexpu-core/-/regexpu-core-1.0.0.tgz",
  "integrity": "sha1-hqdj9Y7k18L2sQLkdkBQ3n7ZDGs=",
  "requires": {
    "regenerate": "^1.2.1",
    "regjsgen": "^0.2.0",
    "regjsparser": "^0.1.4"
  }
},

I understand that carets (^) mean the version is not 100% precise, but I'm trying to figure out WHY my different laptops create different formats for package versions! I checked this SO question which has some great explanations for the differences between ~ and ^, but I didn't find anything explaining why npm would sometimes add and sometimes remove carets (^) altogether. I also looked at this npm issue on Github which recommended looking at npm config settings, but both of my laptops have the same settings:

npm config get save = true (both computers)
npm config get save-prefix = ^ (both computers)
npm config get save-exact = false (both computers)

One laptop was running npm version 5.6.0, but I just updated it to 6.5.0. The other computer was running version 6.4.1, but I also updated it to 6.5.0. I tried running npm install in my project on both computers, but still I find that one computer always removes ^ and the other always adds ^.

Please let me know if there's something I'm missing. Thanks for any help!

After you git pull the revised package.json and package-lock.json onto computer two try deleting the node_modules directory before installing the packages again.

For example: