A close corporation is a type of private corporation that only has a small number of shareholders and are often characterized by owner management and restrictions on the transferability of ownership interests.
There's not much market for shares, and there are restrictions on transferability. Often comes in a form of mandatory buyback provisions - if one owner leaves, the company can buy back his shares before they can be sold in any other way.
There is a specific close corporation statute in Texas (Part 12 of the TBCA) but it's rarely used. The majority of AOIs filed here are generic Close Corporations.
Often similar to partnerships, as all the directors/shareholders and directors (which are necessary in corporations) are all the same people.