No. A disposable email address from SpiderOTP is not a Gmail account, and it does not end in gmail.com. It is an address for receiving an email code from the website you choose.
What is different?
Gmail is an email account you can keep using. A disposable address is intended for a short task and may close. If you need to sign in again or reset a password in the future, use an email address you can keep.
What about Gmail aliases?
A Gmail address with a plus sign, such as name+shopping@gmail.com, still sends mail to the same Gmail account. That is not a separate disposable inbox. Some websites may not accept aliases.
Which should you use?
Use your regular Gmail address for important accounts and recovery. Use a disposable address only when you do not need that email address later, and check that the website accepts it. A verification email is not guaranteed to arrive.