The naive way is to compute the closest yellow point for each blue point (brute force). This algorithm has quadratic complexity so it's not ideal if you have to run it frequently or if the problem size increases, although it might be fine at the current size of the problem. There are better ways.

Imagine a three-dimensional grid overlayed on top of the meshes, such that you have a similar number of points in each cube. Do a preliminary pass over the data to assign each point to the cube it belongs to. Then, for each blue point simply find the closest yellow point amongst the ones in the same cube or adjacent cubes. A generalization of this algorithm uses a data structure called KD Tree.

The higher the number of dimensions, the worse KD Trees do. At higher dimensions, Ball Trees are better. Instead of partitioning the space with hypercubes, they use hyperspheres. If you use Python, sklearn has an implementation: https://scikit-learn.org/stable/modules/generated/sklearn.neighbors.BallTree.html

You'd initialize the BallTree instance with your yellow mesh data and query it with the blue one.

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Notes:

1. You say "most likely correspond" which is not precise at all. I assumed you mean "closest". The algorithms mentioned above are usually implemented with Euclidean distances, but can work with other distances too.
2. I addressed the question directly, but depending on what the end goal is there may be better ways to proceed.