Latent transition analysis uses multiple indicators (items) to extract latent classes and estimates latent transition probabilities from one latent state (class) to another. It is also referred to as latent Markov modeling (see work by Rolf Langeheine and colleagues) because the Markov process is modeled at the latent level, that is, at the level of categorical latent variables that are corrected for measurement error.

Multi-state modeling looks at transition probabilities between observed states, that is, it does not use multiple indicators or latent class variables. For example, it can be used to estimate transition probabilities between being healthy vs. being sick based on a single observed (measured) variable.

The advantage of LTA is that it allows you to correct for measurement error because it is based on multiple indicators. For example, you could model the probably of moving from a healthy state to a sick state by using multiple indicators (e.g. symptoms) of one's physical health.