Which method of logarithmic transformation is correct to use in linear model?

Question

I try to do a simple linear model with logarithmic transformation of y values. I found that depending on which method I use the results differ and I don't understand why. I used 3 different methods:

1. I log10-transformed y values and run a linear model: lm = lm(log10.y ~ x)

    > log10.y = log10(y)
    > lm = lm(log10.y ~ x)
    > summary(lm)

    Call:
    lm(formula = log10.y ~ x)
    
    Residuals:
         Min       1Q   Median       3Q      Max 
    -0.18026 -0.06582  0.01475  0.05069  0.15280 
    
    Coefficients:
                 Estimate Std. Error t value Pr(>|t|)    
    (Intercept) 2.5135003  0.4180387   6.013 0.000319 ***
    x           0.0005840  0.0003388   1.724 0.123027    
    ---
    Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
    
    Residual standard error: 0.1142 on 8 degrees of freedom
    Multiple R-squared:  0.2708,    Adjusted R-squared:  0.1797 
    F-statistic: 2.972 on 1 and 8 DF,  p-value: 0.123

2. I used raw y values and used log-transformation within model call: lm = lm(log(y) ~ x)

    > lm = lm(log(y) ~ x)
    > summary(lm)
    
    Call:
    lm(formula = log(y) ~ x)
    
    Residuals:
         Min       1Q   Median       3Q      Max 
    -0.46187 -0.18506 -0.03391  0.20047  0.40393 
    
    Coefficients:
                 Estimate Std. Error t value Pr(>|t|)   
    (Intercept) 5.3713191  1.1063922   4.855  0.00126 **
    x           0.0018070  0.0008967   2.015  0.07864 . 
    ---
    Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
    
    Residual standard error: 0.3021 on 8 degrees of freedom
    Multiple R-squared:  0.3367,    Adjusted R-squared:  0.2538 
    F-statistic: 4.061 on 1 and 8 DF,  p-value: 0.07864

3. I used raw y values and used log10-transformation within model call: lm = lm(log10(y) ~ x)

> lm = lm(log10(y) ~ x)
> summary(lm)

Call:
lm(formula = log10(y) ~ x)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.20059 -0.08037 -0.01473  0.08706  0.17542 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)   
(Intercept) 2.3327342  0.4805000   4.855  0.00126 **
x           0.0007848  0.0003894   2.015  0.07864 . 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.1312 on 8 degrees of freedom
Multiple R-squared:  0.3367,    Adjusted R-squared:  0.2538 
F-statistic: 4.061 on 1 and 8 DF,  p-value: 0.07864

As you can see, models differ between a model with pre-transformed y values lm = lm(log10.y ~ x) and log transformation within the models (2nd and 3rd method). Model lm = lm(log(y) ~ x) and lm = lm(log10(y) ~ x) only differ in intercept and slope, but the overall models are the same which is logical. But I don't understand why there is a difference in whether I first transform data log10.y = log10(y) and use it in the model lm = lm(log10.y ~ x) or use transformation in the formula directly lm = lm(log10(y) ~ x?

I'd be grateful for any help and explanation.