There is a vast difference between the two as a conceptual paper talk about something new, something which has not been discussed yet. Whereas, in a research paper, you work on the existing researches. You tend to find the research gap and talk about that gap in your study.

The following sections are covered under a conceptual paper:
Research problem, Research objective(s), Research question(s), Literature Review including Theories, Theoretical Framework(s) etc. Whereas, a research paper includes the above plus the following sections:
Research Methods – instrument developed / adopted / adapted, sampling, pilot study, data collection, Data Analyses, Results & Findings, Discussion, Conclusion (including research limitations, recommendation for future research etc.)