# Comparing coefficients in between linear and linear mixed effects models

I have a naive question, but it will help me to get a better conceptual understanding of how the mixed-effects model works.

Question: If I do linear regression and linear mixed-effects regression on the same data (as summarized below), then how can I compare/interpret the estimates from the linear regression to the estimates of the fixed effects from the mixed model? Can I say that estimates of the fixed effects are independent of the estimates of the random effect in a mixed model, which is included in a simple linear model? Or it's the other way around.

Any explanation would be helpful. Thanks.

Linear Model

Call:
lm(formula = pSHP2 ~ condition, data = dat_stim_unstim)

Residuals:
Min      1Q  Median      3Q     Max
-3.6408 -0.5963 -0.1943  0.5046  6.9230

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)    0.583864   0.001941  300.83   <2e-16 ***
conditionstim -0.106348   0.002609  -40.77   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.7409 on 326360 degrees of freedom
Multiple R-squared:  0.005066,  Adjusted R-squared:  0.005063
F-statistic:  1662 on 1 and 326360 DF,  p-value: < 2.2e-16

Linear Mixed Effects Model

Linear mixed model fit by REML ['lmerMod']
Formula: pSHP2 ~ condition + (1 | cluster)
Data: dat_stim_unstim

REML criterion at convergence: 668294.9

Scaled residuals:
Min      1Q  Median      3Q     Max
-5.9819 -0.7061 -0.2411  0.6576 10.0387

Random effects:
Groups   Name        Variance Std.Dev.
cluster  (Intercept) 0.09619  0.3101
Residual             0.45352  0.6734
Number of obs: 326362, groups:  cluster, 24

Fixed effects:
Estimate Std. Error t value
(Intercept)    0.719139   0.063388   11.35
conditionstim -0.097682   0.002375  -41.14

Correlation of Fixed Effects:
(Intr)
conditinstm -0.022
$$`$$