Question: I'm a bit confused whether these two are the same concept. If they are different what's the difference?

Thanks!

Answer: 
Suppose you have a set of binary observations $Y\_i$ for $i=1,\ldots,n$ and, for each observation, an associated explanatory variable $X\_i$. Logistic regression assumes 
$$ Y\_i \stackrel{ind}{\sim} Ber(\pi\_i), \quad \ln\left(\frac{\pi\_i}{1-\pi\_i}\right)=\beta\_0+\beta\_1 X\_i.$$
If you are obtaining point estimates of the parameters via maximum likelihood, then you just use the assumptions above. But, if you are obtaining estimates of the parameters using a Bayesian approach, then you need to define a prior for $\beta\_0$ and $\beta\_1$, call it $p(\beta\_0,\beta\_1)$. This prior along with the logistic regression assumptions above is Bayesian logistic regression.
I don't claim to be an expert on Logistic Regression. But I imagine it goes something like this - suppose $Y$ is a binary random variable taking on either the value $0$ or $1$. Define
$$\pi=\mathbb{P}\left(Y=0∣X\right)\text{,}$$
where $X$ is the independent variable (I'm assuming only one predictor for simplicity). Then logistic regression assumes the form
$$\ln\left(\dfrac{\pi}{1-\pi}\right)=\beta\_0+\beta\_1 X + \epsilon$$
where $\epsilon$ is independent from $X$ and has mean $0$, and the $\beta\_i$ are estimated using maximum likelihood. With Bayesian logistic regression, I imagine you use something like
$$\pi = \dfrac{\mathbb{P}\left(X = x\mid Y = 0\right)\mathbb{P}\left(Y = 0\right)}{\displaystyle\sum\limits\_{j}\mathbb{P}\left(X = x\mid Y = j\right)\mathbb{P}\left(Y = j\right)}$$and assign something for the distribution of $X \mid Y = j$ and a **prior** distribution for $Y$. This is, from my limited understanding, I believe the basis of Linear Discriminant Analysis.