Boolean operators vs Bitwise operators

The general rule is to use the appropriate operator for the existing operands. Use boolean (logical) operators with boolean operands, and bitwise operators with (wider) integral operands (note: False is equivalent to 0, and True to 1). The only "tricky" scenario is applying boolean operators to non boolean operands.
Let's take a simple example, as described in [SO]: Python - Differences between 'and' and '&':
5 & 7 vs. 5 and 7.

For the bitwise and (&), things are pretty straightforward:

5     = 0b101
7     = 0b111
-----------------
5 & 7 = 0b101 = 5

For the logical and, here's what [Python.Docs]: Boolean operations states (emphasis is mine):

(Note that neither and nor or restrict the value and type they return to False and True, but rather return the last evaluated argument.

Example:

>>> 5 and 7
7
>>> 7 and 5
5

Of course, the same applies for | vs. or.

Boolean 'and' vs. Bitwise '&':

Pseudo-code/Python helped me understand the difference between these:

def boolAnd(A, B):
    # boolean 'and' returns either A or B
    if A == False:
        return A
    else:
        return B

def bitwiseAnd(A , B):
    # binary representation (e.g. 9 is '1001', 1 is '0001', etc.)

    binA = binary(A)
    binB = binary(B)



    # perform boolean 'and' on each pair of binaries in (A, B)
    # then return the result:
    # equivalent to: return ''.join([x*y for (x,y) in zip(binA, binB)])

    # assuming binA and binB are the same length
    result = []
    for i in range(len(binA)):
      compar = boolAnd(binA[i], binB[i]) 
      result.append(compar)

    # we want to return a string of 1s and 0s, not a list

    return ''.join(result)

Logical Operations

are usually used for conditional statements. For example:

if a==2 and b>10:
    # Do something ...

It means if both conditions (a==2 and b>10) are true at the same time then the conditional statement body can be executed.

Bitwise Operations

are used for data manipulation and extraction. For example, if you want to extract the four LSB (Least Significant Bits) of an integer, you can do this:

p & 0xF