There are differences between a paint and solid color stain that are recognizable. Recognizing those differences isn't easy.
1) Is there any peeling. A stain shouldn't peel. Although an acrylic solid stain can under certain circumstances.
2) If there is some peeling, carefully remove a piece of the peeling coating and look at its underside. Most likely it will be a light color or white. This could be primer. Only a paint needs primer.
3) Paint, being a surface coating, has a different look and feel than a stain. Paint is thicker than a stain. Plus, a stain could be brittle while a paint (acrylic) is flexible.
4) The thicker nature of paint will fill in many surface cracks and level out some raised grain. Solid stain will leave the cracks mostly open and the raised grain is left intact.
Basically, it all comes down to feeling the difference. A paint will be slick.