data() {
 return {
  loginWay: true 
 }
}

<h2 class="login_logo">用户登录</h2>
 <div class="login_header_title">
  <a href="javascript:;" rel="external nofollow" rel="external nofollow" rel="external nofollow" :class="{on: loginWay}" @click="loginWay = true">短信登录</a>
  <a href="javascript:;" rel="external nofollow" rel="external nofollow" rel="external nofollow" :class="{on: !loginWay}" @click="loginWay = false">密码登录</a>
 </div>

<div :class="{on: loginWay}">
 <section class="login_message">
  <input type="tel" maxlength="11" placeholder="手机号">
  <button disabled="disabled" class="get_verification">获取验证码</button>
 </section>
 <section class="login_verification">
  <input type="tel" maxlength="8" placeholder="验证码">
 </section>
 <section class="login_hint">
  温馨提示：未注册帐号的手机号，登录时将自动注册，且代表已同意
  <a href="javascript:;" rel="external nofollow" rel="external nofollow" rel="external nofollow" >《用户服务协议》</a>
 </section>
</div>
<div :class="{on: !loginWay}">
 <section>
  <section class="login_message">
   <input type="tel" maxlength="11" placeholder="手机/邮箱/用户名">
  </section>
  <section class="login_verification">
   <input type="tel" maxlength="8" placeholder="密码">
   <div class="switch_button off">
    <div class="switch_circle"></div>
    <span class="switch_text">...</span>
   </div>
  </section>
  <section class="login_message">
   <input type="text" maxlength="11" placeholder="验证码">
   <img class="get_verification" src="/UploadFiles/2021-04-02/captcha.svg">

显示效果如下所示：

 
总结