As the comments discuss, a website does not amount to a trademark. However, there are some websites that have become so recognizable that they have gained what is termed secondary meaning, implying that when you see it - you obviously relate to the 'brand.' As an example, "Amazon.com" is a website address that is now a registered trademark.
In most cases, you can register your domain name, even with a letter difference. You should note that acts that are or tend to confuse the consumer may cause you problems. When you need to protect your brand or brand name, it is advisable to contact an attorney and have your potential trademark researched and protected. That way, you have a keen sense of non-confusion with another mark and the peace of mind to focus on your business.
This is not a legal advice as I do not have an attorney-client privilege with you. You should retain a lawyer before acting on any generally available advice.
Maybe? I mean, if your site is PixarTwo, you're probably going to get sued (and by probably, I mean, "You might as well camp out by your mailbox waiting for the cease and desist letter"). If it's JohnsArt and the other site is JohnSmithsArt, you might have more leeway. It's going to depend on a lot of things. Go and see a trademark attorney. He or she can figure out what's going on for you and help you determine out what your next steps should be. You might have to give up on the domain name. That's just the way it works - it's why lawyers are always telling people to clear their potential brand names before they get attached to them; there's nothing you can do if it's already taken, no matter how cool you think it is, except buy it or come up with something else.
No information you obtain from this answer is legal advice, nor is it intended to be. You should consult an attorney for individualized advice regarding your situation. No attorney-client relationship is formed by my responding to your question.
Domains are not trademarks all by themselves but they can be. For example, Google.com. Here the mark is Google so the domain serves as both. But for example, a website that is NYInjurylawyers.com and points to the website of Smith and Jones, LLP is not a trademark but merely a generic web address.
What you want is to create your own TM for your own goods/services. So long as you are not infinging on another's TM rights and have a legit use for the domain it should be fine.
I advise you to clear and file whatever TM you choose so you will not have an infringement issue later and can then protect your own TM against infringement as well. I will link you to some helpful general info below and most of us here, including myself, offer a free phone consult.
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Your question relates to two issues, the trademark clearance process to see whether a mark is available for adoption, and the related topic of likelihood of confusion. You should consult with an attorney to determine these answers, as it is fact specific and should not be answered in a public forum.
For your reference, I've included links to my free 30-minute webinars on the topics of the Trademark Clearance Process and the Likelihood of Confusion.
This answer does not constitute legal advice, and by answering this question we have not entered into an attorney-client relationship.