How can I structure my undergraduate thesis to include two slightly different projects?
Your thesis can be outlined 4 chapters as follows:

Chapter 1: General introduction and review of literature~ you can divide or combine in background, approach and hypothesis,statement of the problem, justification of the research, and objectives of the research. but both projects only have the same problem statement. so you can separate 2 big parts in this chapter and each part has various sections. 

Chapter 2: Your first project~ Exposing what you did in a logical way. This chapter is concise as you mentioned.

Chapter 3:Your second project~
3.1 Introduction 
3.2 Materials and methods 
3.3 Results and discussion
3.4 Conclusion

Chapter 4: General conclusions and recommendations for both projects conducted~ general conclusion, key innovation, recommendation and future prospects.

The best way to make sure that it had better get consultancy from your supervisor or a mentor who is an assistant of your supervisor.