https://github.com/angular/angular.js/blob/v1.3.15/src/auto/injector.js#L651 Provider is primary. Factory is wrapper over provider. Service is wrapper over factory.

provider_factory_service_Angular_source_code.js

  ////////////////////////////////////
  // $provider
  ////////////////////////////////////

  function supportObject(delegate) {
    return function(key, value) {
      if (isObject(key)) {
        forEach(key, reverseParams(delegate));
      } else {
        return delegate(key, value);
      }
    };
  }

  function provider(name, provider_) {
    assertNotHasOwnProperty(name, 'service');
    if (isFunction(provider_) || isArray(provider_)) {
      provider_ = providerInjector.instantiate(provider_);
    }
    if (!provider_.$get) {
      throw $injectorMinErr('pget', "Provider '{0}' must define $get factory method.", name);
    }
    return providerCache[name + providerSuffix] = provider_;
  }

  function enforceReturnValue(name, factory) {
    return function enforcedReturnValue() {
      var result = instanceInjector.invoke(factory, this);
      if (isUndefined(result)) {
        throw $injectorMinErr('undef', "Provider '{0}' must return a value from $get factory method.", name);
      }
      return result;
    };
  }

  function factory(name, factoryFn, enforce) {
    return provider(name, {
      $get: enforce !== false ? enforceReturnValue(name, factoryFn) : factoryFn
    });
  }

  function service(name, constructor) {
    return factory(name, ['$injector', function($injector) {
      return $injector.instantiate(constructor);
    }]);
  }

  function value(name, val) { return factory(name, valueFn(val), false); }

  function constant(name, value) {
    assertNotHasOwnProperty(name, 'constant');
    providerCache[name] = value;
    instanceCache[name] = value;
  }

  function decorator(serviceName, decorFn) {
    var origProvider = providerInjector.get(serviceName + providerSuffix),
        orig$get = origProvider.$get;

    origProvider.$get = function() {
      var origInstance = instanceInjector.invoke(orig$get, origProvider);
      return instanceInjector.invoke(decorFn, null, {$delegate: origInstance});
    };
  }