Completely depends where you work. I spend a lot of time at a free medical clinic and I sit down with every patient every time they pick up their medications. We typically spend 10-30 minutes (sometimes longer) going over their medications, how to manage their disease state(s), questions, etc. Patients come back every 2-3 months, so I have been able to develop a long lasting relationship. Physicians are on site, so I can talk to them if there is a concern. Granted, this is a different environment than a lot of places.
I also did an APPE rotation in a emergency department. I dealt with patients all day long. In that setting, I didn't see them multiple times (unless they were readmitted in the 2 months I was there - which happened multiple times). Also, clinical work doesn't necessarily mean a ton of direct patient contact in the pharmacy world. Clinical work can be monitoring drug levels, adjusting doses of medications under physician-pharmacist collaborations, etc. I worked directly with patients (medication reconciliation, discharge counseling, etc), but also with the physicians (ex. +urine culture and symptoms but no antibiotic ordered - if we want to start something, here is my recommendation).
Traditional retail settings... a lot of patient interaction is possible, but it depends on the company. I am at a place right now that is really busy (3 pharmacists all day and 7-9 technicians). However, they prioritize getting to know their patients and patient interaction. When parents drop off antibiotics, we find out why the kids taking it and make follow up phone calls. We call to talk to patients after they fill a new prescription to find out how it's working. We do lots of diabetes/ blood pressure/ lipid screenings, and immunizations as well. We also go out into the community and do health fairs, work with the local college of pharmacy, etc.
In a few months I will be working with an ambulatory care pharmacist. Patients with diabetes and other chronic conditions come in for appointments with a pharmacist before seeing the physician. Medication recommendations are made at that time for the physician to review. Patients are regularly seen at the office.
Summary: Where you work dictates what your job is as a pharmacist.