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What is difference(Or relation) between "Latent Class Analysis"and Structural Equation models" and "Latent Growth Curve Models"?

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Latent growth curve models are a kind of structural equation model (but they can also be thought of as a multilevel model).

Latent class models and (most) structural equation models are a kind of latent variable model. In a latent class model, the latent variable(s) is(are) considered to be categorical. In a structural equation model (and a latent growth model) the latent variable(s) is(are) considered to be continuous.

It's possible (but a little unusual) to have structural equation models without latent variables.

This image:

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Which I have taken from http://statmodel.com/features.shtml shows the relationship. y and u are continuous and categorical outcomes. f and c are continuous and categorical latent variables. x predictors. The ellipse of A is conventional structural equation modeling, with continuous latent variables (and one or more of these latent variables can represent a growth term), the ellipse B represents latent class analysis.

(There's also a between layer and within layer - that's the multilevel part).

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