So the tone I'm aiming for is like these:





So I looked in the forum and observed these favourite singers of mine and came to the conclusion that a singer should use his talking voice (cause that is also the 'inner voice' right).

So my talking voice sounds roughly like this:

When I sing, I get a sound like this:

Completely 'not' the tone I want. I need to sound a bit raspy and higher. But how do I do that? Are there any other things I need to achieve my desired tone?
For practice try singing one of the songs you just posted (the calling/goo goo dolls). Record it and then compare.

You will hear exactly what needs to be done yourself.
You have very poor singing technique. Before you can work on timbre, you have to get the fundamentals down: solid breath control, relaxed open mouth and throat, and so on. You don't have that stuff.

Trying to sound any particular way at this point - worrying about "speaking voice" or anything like that - is a complete waste of time. You're basically comparing a dilapidated shack with a mansion and saying, "Hmm, well, the mansion has blue trim around the windows, and I want my shack to be like that mansion, so I'll paint the trim around my one broken window blue."

Find a teacher who's familiar with popular music (eg, not someone who's going to try to teach you to sing show tunes or opera) and take lessons, starting with the absolute basics. The stuff you're worried about here is the window trim color, and you don't even have a foundation yet.

People sound REALLY bad when they try to compensate for lack of fundamental technique by piling on artifice. Don't do that.
^Thank you for being honest. Unfortunately I dont have money to go on singing lessons. Cant i learn the basics online?
I don't know. I don't think so. You could probably find some group lessons that wouldn't be terribly expensive. I honestly think singing is much harder to self-teach than guitar. It doesn't take a ton to get the fundamentals down and be able to work on your technique yourself by recording and listening to yourself.