Python 2, 35 bytes

lambda a,b:(a^b)&-(a^b)in[a^b or[]] 

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Uses the power-of-two check n&-n==n, eliminating the n==0 false positive.

Python 2, 41 bytes

lambda a,b:bin(a^b).count(`+True`)is+True 

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Taking TFeld's lambda a,b:bin(a^b).count('1')==1 and making it pristine by changing the 1's to +True and == to is. Thanks to Jo King for 1 byte.

Python 2, 35 bytes

lambda a,b:(a^b)&-(a^b)in[a^b or[]] 

Try it online!

Uses the power-of-two check n&-n==n, eliminating the n==0 false positive.

For reference, these are the pairs of one-char binary operators that are one bit apart, making them hard to use:

+ / - / * + % - < | < > 

Fortunately, & and ^ are not among these.

Also note that == can become <=, and + can become the comment character #.

Python 2, 41 bytes

lambda a,b:bin(a^b).count(`+True`)is+True 

Try it online!

Taking TFeld's lambda a,b:bin(a^b).count('1')==1 and making it pristine by changing the 1's to +True and == to is. Thanks to Jo King for 1 byte.

Python 2, 41 bytes

lambda a,b:bin(a^b).count(`+True`)is+True 

Try it online!

Taking TFeld's lambda a,b:bin(a^b).count('1')==1 and making it pristine by changing the 1's to +True and == to is. Thanks to Jo King for 1 byte.

Python 2, 35 bytes

lambda a,b:(a^b)&-(a^b)in[a^b or[]] 

Try it online!

Uses the power-of-two check n&-n==n, eliminating the n==0 false positive.

Python 2, 41 bytes

lambda a,b:bin(a^b).count(`+True`)is+True 

Try it online!

Taking TFeld's lambda a,b:bin(a^b).count('1')==1 and making it pristine by changing the 1's to +True and == to is. Thanks to Jo King for 1 byte.

Python 2, 41 bytes

lambda a,b:bin(a^b).count(`+True`)is+True 

Try it online!

Taking TFeld's lambda a,b:bin(a^b).count('1')==1 by changing the 1's to +True. Thanks to Jo King for 1 byte.

Python 2, 41 bytes

lambda a,b:bin(a^b).count(`+True`)is+True 

Try it online!

Taking TFeld's lambda a,b:bin(a^b).count('1')==1 and making it pristine by changing the 1's to +True and == to is. Thanks to Jo King for 1 byte.