What they have in common
Both are diamond, with essentially the same chemical composition, crystal structure and optical and physical properties. A lab-grown diamond is not an imitation stone.
Cut, colour, clarity and carat describe the same characteristics in either. How they are reported can differ: a laboratory may issue a different kind of report for a laboratory-grown diamond than for a natural one, with its own format and terms, so read what the report for a particular stone actually says. How that stone looks still depends on the stone itself — its cut, colour and clarity — so two are not interchangeable merely because they share a category.
Where they differ
The difference is origin. A natural diamond formed deep in the Earth, and natural diamonds can be millions or even billions of years old. A laboratory-grown diamond was grown in controlled conditions.
Several things follow from that, and they are worth keeping apart. Origin is where the stone came from. Identification is how a laboratory establishes which it is: by eye the two may be indistinguishable, and telling them apart can require advanced instruments. Documentation is how the result is recorded. Quality assessment is a separate question, about that individual stone. Price is another question again.
Price and future value
How a particular stone is priced, in either category, is a question for the company selling it.
This is one area to be careful with: nobody can tell you what either category will be worth in the future. Buy the stone because you want to own and wear it, not on the basis of a prediction about later value.
Questions worth asking
Ask which category a stone belongs to and how that is documented. Ask what the accompanying paperwork covers and who issued it.
Ask how the seller handles each category in practice — documentation, warranty and any aftercare are set by the company you buy from, and should be confirmed with them directly before you commit.
Deciding
There is no universally correct answer. Some people care a great deal about natural origin; for others the question is how each category would change the balance between the stone, its visible size and the setting within the same comfortable range.
Both are legitimate choices. The one that matters is the one you will still be comfortable explaining in ten years.