Does internships and residencies necessarily mean 'more' income besides the obvious training and experience?
It depends on the job. In general, a board certified specialist working in a private specialty practice will make more than someone in a general practice because their production is higher. But it depends on the specialty and the practice.
Someone with an internship will be slightly more competitive for a job in general practice compared to someone with 1 year of non-intern experience. But not by a lot and you have to consider the intern has been working for a year at less than minimum wage while the other person has been making a decent salary for that year. In other words, don't do an internship for the money.
While doing a residency, is it possible to be working at a clinic or are residencies done as 'hands on schooling'?
Residencies are clinical training programs. You are working in a hospital under the supervision of specialists.
Are the chances higher for a DVM to get accepted to a position if he/she has that board certified diploma (from the residency/internship)?
You don't automatically get boarded from doing a residency -- there are other requirements such as examinations. But you're comparing apples to oranges because specialists and generalist are not applying for the same jobs. If it's a specialty position, they are going to hire someone who has completed a residency in that specialty and usually someone who is boarded.
If it's a general practice position, they aren't going to hire a boarded specialists, they're looking for a generalist.
And last, what is the major difference between the residency and internship?
Rotating internship -- 1 year clinical training position working in a variety or areas designed to provide additional training for those entering general practice or a residency
Residency -- usually a 3-year clinical training position working primarily in that specialty to provide requirements to become board-certified in that specialty
BTW, there are now also 'specialty internships' where the intern works mostly in that particular specialty. This is usually for people who have already done a rotating internship to help them be more successful in getting a residency in that specialty.