Using correct terminology is important for avoiding misunderstandings. For example, the terms univatiate and multivariate are often misunderstood. The terms refer to the type of probability distribution a model is based on. A univariate statistical model is based on a univariate probability distribution, i.e. it has one outcome variable, and a multivariate analysis is based on a multivariate probability distribution, i.e. the model has multiple outcome variables. An ANOVA model, for example, is univariate and has one outcome variable, but a MANOVA model is multivariate because it has more than one outcome variable.
A regression model can have one or more regressors. A regression analysis with one outcome variable and one regressor is known as a simple regression analysis; with multiple regressors it is a multiple regression analysis. In order to change the common misuse of the description of "multivariate" for univariate multiple regression models, the term "multivariable" has been coined. This term just says that the statistical model includes multiple variabels. In analogy, a simple regression model should have been called bivariable, but it is described as a univariable model.
In summary, even if it is possible to analyse a multivariate multivariable statistical model, most multivariable models are univariate.