Why is this even a thing? All reversible encryption (which in itself is a tautology) is searchable.
Plaintext record ID > Encryption+key+salt etc > Cyphertext record ID. Search for the cyphertext record ID. Bring encrypted record back from database. Encrypted record > Encryption > Plaintext record.
How is this a marketable product?!
Searchable encryption is more complicated than you think. For example if I encrypt the sentence "I like reading slashot" with traditional encryption I will get a block binary data that is meaningless. Now suppose I want to check if that block contains the word "slashdot"? Your "cyphertext record id" approach won't be of much help. You need a few tricks to do it correctly, notably adding some metadata and additional cryptographic mechanisms. To make things more complicated, you often need the encryption mechanism to be "format preserving": if you encrypt a string field you get a string field, if you encrypt a number field you get a number field, while traditional cryptography outputs binary data.
Note that you may have misunderstand how encryption works, if you believe that all reversible encryption is searchable. Good encryption is randomised: if you encrypt the same plaintext twice with the same key you get 2 different cypher-texts (to take your analogy, you must use different salts).