What is the difference between a stratified random sample and a single-stage cluster random sample? Is there a distinction besides the availability of a data frame for a stratified random sample? 
 A: There is one key distinction. Suppose all population units can be classified into a number mutually exclusive groups. 
A stratified sample draws from each group a sample and calls the groups strata (but usually not all units of a stratum are sampled). 
A cluster sample first draws a sample of groups from all groups and calls the groups clusters. It then samples from the units of the sampled clusters (sometimes even all units of a cluster). 
A cluster sample is usually used when the number of groups is large. It usually increases variances of estimators. A stratified sample is used when the number of groups is small. Used properly, it can decrease the variance of estimators.
A: In the stratified random sampling, we stratify the sample into $N$ groups and then use some other sampling method like simple random sampling to choose $M$ cases from each group for a total of $N*M$ observations, while in single-stage cluster random sampling we cluster the sample into $K$ groups and then use some other sampling method like simple random sampling to choose $k$ clusters(including all observations in those clusters). 
When we don't know how to stratify the sample and sampling in that way is expensive and the diversity in each cluster is large we can choose clustering sampling even if we need more complicated methods to analyze those observations. 
