For the purposes of being affected by effects, it depends on the creature
Depending on the creature, the shapeshifting ability usually describes which statistics are kept and which are not. For more details on what counts as statistics you can see this question. The statistics are what determines what a creature counts as.
For example, the werewolf states that (emphasis mine):
The werewolf can use its action to polymorph into a wolf-humanoid hybrid or into a wolf, or back into its true form, which is humanoid. Its statistics, other than its AC, are the same in each form.
So, in the case of the werewolf, since the stat block states that it is a Medium humanoid (human, shapechanger) (this is the creature type and tags, part of the statistics), and this is not changed when shapeshifting, you could not use something like dominate beast on a shapeshifted werewolf, a spell that targets beasts and affects normal wolves (which are beasts).
Contrast this with, for example, an Ancient Gold Dragon whose change shape ability states:
In a new form, the dragon retains its alignment, hit points, Hit Dice, ability to speak, proficiencies, Legendary Resistance, lair actions, and Intelligence, Wisdom, and Charisma scores, as well as this action. Its statistics and capabilities are otherwise replaced by those of the new form, except any class features or legendary actions of that form.
In this case, the Dragon's type does change to whatever it is transforming into (humanoid or beast in this case) so it does become a valid target for effects that target only those creature types