What is the difference between ui-bootstrap-tpls.min.js and ui-bootstrap.min.js?

So, ui-bootstrap-tpls.min.js == (ui-bootstrap.min.js + HTML templates) required by the JavaScript code. If you only included ui-bootstrap.min.js, you will also need to provide your own HTML templates.

Otherwise you will see something like:

GET http://localhost:8989/hello-world/template/tooltip/tooltip-popup.html 404 (Not Found) angular.js:7073
Error: [$compile:tpload] http://errors.angularjs.org/undefined/$compile/tpload?p0=template%2Ftooltip%2Ftooltip-popup.html
    at Error (<anonymous>)
    at http://localhost:8989/hello-world/js/vendor/angular-1.2.0-rc.3/angular.min.js:6:453
    at http://localhost:8989/hello-world/js/vendor/angular-1.2.0-rc.3/angular.min.js:54:14
    at http://localhost:8989/hello-world/js/vendor/angular-1.2.0-rc.3/angular.min.js:64:438
    at A (http://localhost:8989/hello-world/js/vendor/angular-1.2.0-rc.3/angular.min.js:89:258)
    at A (http://localhost:8989/hello-world/js/vendor/angular-1.2.0-rc.3/angular.min.js:89:258)
    at http://localhost:8989/hello-world/js/vendor/angular-1.2.0-rc.3/angular.min.js:90:465
    at g.$eval (http://localhost:8989/hello-world/js/vendor/angular-1.2.0-rc.3/angular.min.js:98:272)
    at g.$digest (http://localhost:8989/hello-world/js/vendor/angular-1.2.0-rc.3/angular.min.js:96:142)
    at g.$apply (http://localhost:8989/hello-world/js/vendor/angular-1.2.0-rc.3/angular.min.js:99:100)

The tpls tag means that the file also contains templates.

Here is an example:

ui-bootstrap.js

angular.module("ui.bootstrap"
 ["ui.bootstrap.transition"
"ui.bootstrap.collapse"
"ui.bootstrap.accordion"
"ui.bootstrap.alert"
"ui.bootstrap.bindHtml"
"ui.bootstrap.buttons"
"ui.bootstrap.carousel"
"ui.bootstrap.position"
"ui.bootstrap.datepicker"
"ui.bootstrap.dropdownToggle"
"ui.bootstrap.modal"
"ui.bootstrap.pagination"
"ui.bootstrap.tooltip"
"ui.bootstrap.popover"
"ui.bootstrap.progressbar"
"ui.bootstrap.rating"
"ui.bootstrap.tabs"
"ui.bootstrap.timepicker"
"ui.bootstrap.typeahead"]);
angular.module('ui.bootstrap.transition'
 [])

ui-bootstrap-tpls.js

angular.module("ui.bootstrap"
 ["ui.bootstrap.tpls"
 "ui.bootstrap.transition"
"ui.bootstrap.collapse"
"ui.bootstrap.accordion"
"ui.bootstrap.alert"
"ui.bootstrap.bindHtml"
"ui.bootstrap.buttons"
"ui.bootstrap.carousel"
"ui.bootstrap.position"
"ui.bootstrap.datepicker"
"ui.bootstrap.dropdownToggle"
"ui.bootstrap.modal"
"ui.bootstrap.pagination"
"ui.bootstrap.tooltip"
"ui.bootstrap.popover"
"ui.bootstrap.progressbar"
"ui.bootstrap.rating"
"ui.bootstrap.tabs"
"ui.bootstrap.timepicker"
"ui.bootstrap.typeahead"]);

angular.module("ui.bootstrap.tpls"
 ["template/accordion/accordion-group.html"
"template/accordion/accordion.html"
"template/alert/alert.html"
"template/carousel/carousel.html"
"template/carousel/slide.html"
"template/datepicker/datepicker.html"
"template/datepicker/popup.html"
"template/modal/backdrop.html"
"template/modal/window.html"
"template/pagination/pager.html"
"template/pagination/pagination.html"
"template/tooltip/tooltip-html-unsafe-popup.html"
"template/tooltip/tooltip-popup.html"
"template/popover/popover.html"
"template/progressbar/bar.html"
"template/progressbar/progress.html"
"template/rating/rating.html"
"template/tabs/tab.html"
"template/tabs/tabset-titles.html"
"template/tabs/tabset.html"
"template/timepicker/timepicker.html"
"template/typeahead/typeahead-match.html"
"template/typeahead/typeahead-popup.html"]);
angular.module('ui.bootstrap.transition'
 [])

For example: template/alert/alert.html

angular.module("template/alert/alert.html", []).run(["$templateCache", function($templateCache) {
  $templateCache.put("template/alert/alert.html",
    "<div class='alert' ng-class='type && \"alert-\" + type'>\n" +
    "    <button ng-show='closeable' type='button' class='close' ng-click='close()'>&times;</button>\n" +
    "    <div ng-transclude></div>\n" +
    "</div>\n" +
    "");
}]);

People have answered this question already, but I wanted to point out that starting with release 0.13.4, we've added the ability to provide your own templates on a case-by-case basis (i.e., each directive use, not application wide, though, the latter would not be hard to do).