What kind of animal we have?

[the lynx]

Holy crap! I sure hope not it is one of those.

Nope. A standard, non-speckled, beige type, just pretty large.

Then I can imagine the sound from this fellow. Yeah, they do sound close to what you have described. Loud or not, depends on your proximity and the location (louder when they are out in open, and muffled when they are behind furniture).