Are linseed oil paint and oil paint the same thing?

No. This is a common misconception, and we cannot stress the difference enough. Linseed oil paint can be applied without using a solvent. Oil paint, on the other hand, is based on a modified oil (often a synthetic alkyd oil) and requires solvents to be paintable. Sometimes, such oil paints can be marked with “linseed oil”, but these contain only a very small addition of linseed oil.