Do cluster labels have any significance to "distance" between clusters?

I am using "cluster" on a set of 300 vectors, each vector 1 x 10. They are arranged into a 300 x 10 array. I input my data to the cluster function, and use the 'Criterion' of 'distance'.

Does the number that matlab assigns each cluster necessarily have anything to do with the "distance" between clusters? For example, if my code outputs 20 clusters, are clusters 19 and 20 "closer" than clusters 1 and 20?

I am asking because the clustering outputs a trimodal "distribution" of clusters, and one of the large clusters is labelled as 2 and the other large clusters are labelled 18 and 20. Empirically, the data used to generate the 18th and 20th clusters have much more similar qualitative characteristics, so this type of labeling would make sense, but I dont want to draw this conclusion without evidence.

I.e. does the numerical label given during clustering have any quantitative basis?