My official title is a Network administrator. I pretty much go out on trouble calls, patch security holes, and help out with administrating some of our network encryption gear, setting up fiber paths, and occasionally messing with switches. Have I described the job of a sys admin or a IT Consultant? What's the difference?
I would be inclined to give the role you describe the title "Network Administrator". It doesn't sound there is involvement with servers or core equipment, so I might prefix it with "Junior".
"Consultant" is a generic term and can apply to anything. Generally, it implies vendor rather than employee, temporary assignments rather than permanent duties, and the giving of advice or recommendations rather than execution.
I disagree with l0c0b0x that "IT consultant and SysAdmin go hand". Consultants might give advice on SysAdmin stuff, and SysAdmins might be called to give advice on their area of expertise, but the actual responsibilities only overlap slightly.
That pretty much fits the description of a sysadmin's job.
Although I can't say I know exactly the job description that would fit an IT consultant, the consultants are usually hired from outside. They do not work on a payroll in a company. For example, a systems engineer which was hired to help install a new system (like SAP) would be my definition of IT consultant.
The actual workload and expertise would be similar, though based on my experience, I would expect an IT Consultant to be an independent contractor, work with high-level officers in the organization, and not have a manager. I'd consider a system administrator to be staff, have a manager, and rarely interact directly with high level management.
I think you described the job of a Network Administrator. Not a System administrator because you never mention any type of system that you would administer, except for your comment that you "patch security holes" which is a pretty vague statement. I really wouldn't consider you a consultant either because consultants typically are hired on a short contract or temporary basis, where you specialize in a specific area (HP hardware tech, Dell hardware tech, Terminal Server tech, VMware tech, etc.), and you didn't describe anything in your job which fits you into that position.
I'm not sure how big of an IT department you have where you are, but typically in larger environments IT is broken up into multiple areas Network Admins, Network Engineers, System Admins, System Engineers, Help Desk, etc. But when it comes to smaller environments you can play the roles within IT, for example the Help Desk, Network Admins and System Admins could be coupled into one job. Where I work at we have around 30-40 IT guys so we are broken up into the different titles that I listed above, which keeps us focused on certain specialties within our infrastructure.
Consultants are temporary workers. They are usually either direct contract or brought in as part of a larger contract between two companies.
The "IT Consultant" title is pretty nebulous and can just as easily be focused on development, administration, design, or even just operations. In other words, it's very generic and is almost always appended with something like "for Networking"; as in, "I just brought in a couple IT Consultants to help with our network."
Now, if you are frequently billed out to complete work for other companies or individuals then congratulations, you are now an IT Consultant. If, on the other hand, your work is solely for the company you are currently employed with, then based on your job description you are a Network Admin.
I call myself an IT Administrator, because I do servers (~100 total) and networks (~6/7 WAN links) across 4 physical sites.
A consultant is, in my view, someone hired by the company to accomplish a specific task, where as a full time position of monitoring and maintaining the infrastructure would be considered outsourcing.
As an IT consultant myself, i hope i know what i'm doing ;) I am working for a company, which also does selling of software/appliances. The consultants in the company are asked in house by salespeople on ideas/advice/estimations and plan projects for customers. Besides that, i do execute, program and also administrate servers. I wouldn't consider programming (rather than designing the software) or administering servers for our customer as part of the consulting job. It's just that in real life, what counts is practicality ;)
In my mind Administrators handle day to day tasks and needs of an organization. These positions tend to be internal. A consultant as some have mentioned before is a bit nebulous but typically they're called in with an area of expertise outside of the current operations staff.
The consultant can be a higher level "architecture" role or the nuts and bolts of a complex system in place (or implementation of a new system). A consultant might be called in because the organization is planning to make changes (which are outside the experience of the administrators) and they want someone who has been in different environments and has experience in what does and doesn't work. Naturally the quality of different consultants vary depending on how much experience they have and how sharp they are.