What encryption options are available in SQL server standard edition?
If you have SQL Server Standard edition then you do not have Encryption built into the product.  You have other options as the articles you reference mention, but they require work on your part to implement.  

I think the confusion is where you are seeing that you can implement column/cell encryption using Enterprise edition OR through alternative methods.  Those alternative methods are:


Triggers and CLR functions to do the encryption/decryption for you.  
Using the application layer to encrypt/decrypt the data on read and
write to/from the database.


The advantage to using TDE is that SQL understands the encryption and you can search on the encrypted data directly because it is only encrypted on disk.  But if you have encrypted the data using CLR or the application then you cannot do that and must decrypt every row.  

Encryption is hard, don't roll your own.  Find out what is required by the business, not managements "everything must be encrypted" and work towards that.  You may be able to get away with seeing if the storage layer has encryption that can be implemented.