Business credit cards are offered to businesses. The application will have a section for the business applying and the underlying officer or owner that looks very similar to a personal credit card application. Individuals, even those without real businesses, can apply for business credit cards using their SSN as the Tax ID number and applying as a sole proprietorship (your title would be "Owner"). If you were ever asked what your business is, you could say you sell things on
Amazon. Personally, I say my business is "[my real job] consultant". For business income, list at least $1,000 (I use 10% of my actual income). For time in business list 1 year -- this way you can say it is a new business and your business income is your anticipated income (e.g. no business tax returns filed). I have never been asked any of these questions by Amex or Chase -- and only once was I asked to confirm my business mailing address (same as my home address).
5/24 refers to Chase's credit card restriction that you can only be approved for 5 personal credit cards (across all credit card issuers) in a 24 month time period. If you reach 5/24, then Chase will automatically deny you for new credit cards (business or personal). Amex business cards do not report to your personal credit, so Chase doesn't count them towards the 5 card limit (Chase also does not count their own business credit cards -- which is why you see members here applying for their business Ink products regularly to get more cards).
It may seem intimidating at first, but business cards are the real secret to maximizing credit card rewards because you double or triple the number of sign up bonuses you can get over time (particularly with Amex's 1 bonus per card per lifetime rule and Chase's 5/24 rule). Most issuers have business credit cards and most don't count towards 5/24 (Capital One being the exception amongst major companies).
Hope this helps.