My basic knowledge would assume yes, unless websites somehow include the user name into the hashing function with the password, but I am not sure if this is common practice.
As always, a good read is Thomas Pornin's canonical answer to How to securely hash passwords, which gives both advice and explanations on unique per-user cryptographically random salts, with PBKDF2, BCrypt, and SCrypt being algorithms of choice and said salts being mandatory.
For your particular question, simply read through the security.stackexchange.com and stackoverflow.com questions with the "passwords" tag, and you will quickly find that there is NO standard way of doing anything with passwords.
SCrypt is nearly unknown.
BCrypt is mostly reserved for PHP 5.5 and up (and 5.3.7 with password_compat; there's a good number of PHP folks using it, and a good number of PHP folks using something else.
PBKDF2 is the good choice for nearly everyone else.
And you STILL have a combination of other iterated hash methods (often with salting mistakes), single iterations of a hash (usually with salting mistakes), unsalted hashes, and out and out Don't be a Dave questions, over and over and over and over and over again.
So no; when it comes to actually dealing with passwords, you should assume that Dave is coding your website.