Semi-log and log-linear models are terminologies used in Econometrics. They are not the same.
Log-linear models
$$
Y = e^{\beta _1 }X_2 ^{\beta _2 }X_3 ^{\beta _3 }e^\epsilon
$$
it is linearized as
$$
\log Y = \beta_1 + \beta_2 \log X_2 +\beta_3 \log X_3 +\epsilon
$$
Here $\beta$-coefficients are elasticities. For this reason, the log-linear model is also known as the "constant elasticity model".
Semilog-linear models
these are useful when coefficients are interpreted as relative variations (rate of change). The original model is
$$
Y = \exp\left(\beta _1 +\beta _2 X_2 + \beta _3 X_3 + \epsilon\right)
$$
and it is linearized as
$$
\log Y = \beta _1 +\beta_2 X_2 + \beta_3 X_3 + \epsilon
$$
In this case
$$
100 \times (\exp(\beta_k) - 1)
$$
measures approximately the expected percentage change in $Y$ for a unit change in $X_k$ holding all else equal.
R squared interpretation
If you fit a linear model that is a linearized version of a non-linear model the $R^2$ must be carefully handled.
The $R^2$ is the fraction of variability of the outcome variable (or dependent variable) captured by the regression function. But the previous is referred to the linear model.
Now, for the previous log-linear model the outcome variable is $\log Y$ while the regression function is $\beta_1 + \beta_2 \log X_2 +\beta_3 \log X_3$
In the case of the semilog-linear model example, the outcome is again $\log Y$, while the regression function is $\beta _1 +\beta_2 X_2 + \beta_3 X_3$.
Side comment on the use of the $R^2$
The $R^2$ is one of the most dangerous tools. It's almost worthless and should be removed from any introductory-intermediate statistics book. People use it following silly rules of thumb, but there are serious technical issues why its misuse can be dangerous.
Intuition: suppose you run a regression and you find a spectacular $R^2 = 0.999999999999....$ approaching its "ideal maximum value". You are happy, but this means that the estimated variance of error term in the regression is close to 0... this is a violation of the assumption that your observed outcome $Y$ is a random fluctuation around the conditional mean of $Y|X$ represented by the (linear) regression function.
In the best case, a too good $R^2$ is an indication that you are fitting noise, then the question is: how large should be $R^2$ before to worry about it? Nobody knows the answer, because this depends on the bias-variance trade-off. Since of this I strongly suggest looking at other better measures of fitting.