The following table lists common “portmanteau” names for linear models. Note that different traditions/disciplines might use one particular name more often than the others.

My usual recommendation is to move away from using specific names like “logistic regression” or “mixed-effects models” and instead just specify what kind of components your linear model has (see the Description column in the table).

Formula Description Names
lm(y ~ x) Linear model with one predictor x using a Gaussian distribution for the outcome variable y simple linear regression, simple linear model
lm(y ~ x + z + ...) Linear model with two predictors or more using a Gaussian distribution for the outcome variable y multiple linear regression, multiple linear model
glm(y ~ x + ..., family = "binomial") Linear model with one or more predictors using a Bernoulli distribution for the outcome variable y logistic regression, binomial regression, general(ised) linear model
lmer(y ~ x + ... + (1 | z)) Linear model with one or more predictors, including one or more random intercepts, using a Gaussian distribution for the outcome variable y. mixed-effects models, nested models, hierarchical models, multilevel models, cross-effects models (plus combinations of those and “linear” or “regression”)
lmer(y ~ x + ... + (w | z)) Linear model with one or more predictors, including one or more random intercepts and one or more random slopes, using a Gaussian distribution for the outcome variable y. Same as above. Sometimes “random-slope models”
glmer(y ~ x + ... + (w | z), family = "binomial") Linear model with one or more predictors, including one or more random intercepts and one or more random slopes, using a Bernoulli distribution for the outcome variable y. Same as above, but includes “logistic”, “binomial” or “general(ised)” in the name
glm(..., family = "poisson") Linear model with one or more predictors, including one or more random intercepts and one or more random slopes, using a Poisson distribution for the outcome variable y. Same as above but includes “Poisson” in the name

Note: When specifying the binomial family in glmer(), the Bernoulli family is selected automatically under the hood