>or did i interpret it wrong and I would need last full backup file + differential 2 + log file 2.1 + log file 2.2....

I have not read the blog but above one seems correct approach. Differential backup is *mainly* there to reduce Recovery Time Object(RTO) it reduces the time taken to bring database up and running after disaster strikes.

**Example:**

If you have 

1. Daily full backup 
2. Every 4 hr differential backup
3. Every 15 mins log backup

Suppose your database crashes `today at 5 PM.`

The restore sequence would be

First restore Today's full backup with no recovery then 4 PM differential backup with no recovery and the  all log backup with no recovery, just the last log backup with recovery to bring database online.

If in above scenario you dont take diff backup then restore sequence would be

Todays full backup and then all log backups taken after this full backup witn no recovery just the last backup with recovery to bring DB online.

>What is contained in differential backup, is it just mdf + ndf backup or ldf + mdf + ndf backup since last full backup was taken?

You added above part of question after my answer so I will include this as well.Differential backup includes are all the data extents that have changed since the last full backup. Yes they also include (if required) few amount of transaction log to bring database into consistent state after restore is done. For more details [read this][1] 


  [1]: http://www.sqlskills.com/blogs/paul/a-sql-server-dba-myth-a-day-3030-backup-myths/