Everybody has feet, and the vast majority of people will have foot pain, injury, etc at some point... so everyone is a potential patient. Look at the foot care aisle at drug stores: everything from toe splints and pads to wart treatments to insoles to ankle braces to antifungals.
Each DPM's patient population varies based on what they are trained for and how they market their practice. If you clip a lot of toenails for old folks, you will get more and more of that since patients talk to friends, family, etc and will recommend you. There's a saying: "like refers like." If you do good diabetic wound care, your rep and referral base for that will probably tend to grow. It's the same for sports med... reconstructive surgery... peds... foot and ankle trauma... diabetic surgery... etc etc.
You are exposed to all of those things during pod school, and it's up to you as to what you will focus on, in residency training and in practice. If you are in a rural area, you will probably do a bit of everything since you will possibly be the only DPM, and therefore, the best guy for the job. If you are in a big city, you will still have to do it all, but you can probably market and network your practice to play towards your training strengths and personal interests. If you are residency trained with a lot of rearfoot trauma, then you will probably try to do more of that and less primary podiatric care. If you did a program that was mostly forefoot and derm care, then that is likely what you will be most comfortable with, and you may refer out other cases. Wound care gurus will probably make a point to get in with wound care centers, get on staff to consult at hospitals, network with endocrinologists and plastics, etc. If you like working with athletes, then it may be smart to structure your practice around getting team or schools to send you referrals for those injuries, orthotics, etc. It's really up to you...