1. Any procedure that is labeled as univariate means you have a single dependent variable.
2. Any procedure that is labeled as multivariate means you have two or more dependent variables.
3. Any procedure that is labeled as "multivariable" implies two or more variables are involved. As applied to regression models, in my experience, people apply this to the count of IVs (independent variables).
4. I don't have a good answer for "monovarietal" logisitic regression. "Simple logistic regression" implies one IV. "Monovariable" logistic regression would also imply one IV (see #3). Monovarietal sounds like a term better suited for zoological taxonomic classification.
An univariate logistic regression is a model with only one depend variables.
A multivariate logistic regression is a model with more than one dependent variables.
Monovarietal and multiple variate are not common labels, but I would guess they are synonym of univariate and multivariate. I never read anyone using those labels.
1. Hidalgo, B., & Goodman, M. (2013). Multivariate or multivariable regression?. American journal of public health, 103(1), 39–40. https://doi.org/10.2105/AJPH.2012.300897
3. Article( Developing a Multi-variate Logistic Regression Model to Analyze Accident Scenarios: Case of Electrical Contractors Pouya Gholizadeh * and Behzad Esmaeili)