A label reading simply 'Chinese orchid' leaves too much unanswered. It does not establish the species, flowering habit or growing conditions of the plant in front of you.
Ask for the botanical name or the original nursery identification. Keep that information together with a photograph of the plant and its label. Translating a common name from memory can introduce another layer of confusion.
Use flowers and leaves as supporting evidence
A leaf count or a reported flowering month can help narrow a comparison, but neither should overrule a reliable identity on its own. Plants differ with age, condition and the place where they are grown.
Before choosing a potting medium or a winter position, find care information for the identified orchid. Instructions for a supermarket phalaenopsis are not automatically instructions for a terrestrial cymbidium.
If the seller cannot identify it, decide whether you are comfortable buying an unknown plant. A low price does not make its requirements clearer. For a first orchid, an accurately labelled plant with a care history is often a more useful purchase than an unnamed 'rare' variety.
Related reading: Chinese Orchids: An Introduction to Common Garden Types.