Remodel means take out what you have and put in something new. So, you use the same space, but different options. For example, removing an old cabinet and putting something newer in is remodeling.

In reality, the end result of a refurbish or a remodel is the same, the space looks better, and fresher. However, there are some major differences. For example, when you refurnish, you generally update for less cost than you do when you remodel.

Let's look at this a little closer:
If you have an older home, to refurbish it would mean to restore it. In other words, you would want to keep original fixtures, original style, the feel of the period etc. But you would update plumbing, update electrical, use brass cleaners to make fixtures shine, apply fresh paint in the colors of the period. Install new flooring, but keep it in theme with the time and period.

Now, if you were to remodel this same house, you would likely use a whole different color scheme. You would modernize. You would replace old fixtures with new streamlined fixtures. Instead of refinishing the classic tub, you would replace it with a larger, jetted tub. The idea with remodel is to update, and make modern. The ideas with refurbish is to update and make usable, but maintain the feel of the period.

Let's take a look at some of the areas in your home you would need to make a decision about refurbishing or remodeling:

The kitchen.
To remodel the kitchen, you would likely replace an old porcelain sink with a new, divided, stainless steel sink. You would either install all new cabinets, or sand, paint, or re-stain, and replace all existing hardware with something fresh and new. You would likely pull up and replace all flooring, although this depends on what type of flooring it is.

If you refurbish instead, you can give your kitchen an updated feel by refacing cabinets, resurfacing countertops and replacing worn flooring with something similar that fits the same time period, but is new. That's going to be a whole lot cheaper than ripping out all the cabinetry and starting over, and it maintains the look and feel of the home while bringing it up to date, and giving it some modern conveniences.

The bathroom.
To remodel a bathroom you would likely replace the tub, add a new shower head, or a separate shower. You would likely install a new, elongated toilet, a new vanity and sink area. You may leave existing tiling depending on the condition, but you may just gut it and re-do floors, walls, etc.

To refurbish a bathroom you would likely resurface the tub, re grout to give the tiling on the walls a fresh feel, but maintain the look. You would likely change out faucets etc. but replace them with period appropriate ones, or you may simply clean them really well, refinish them, and return them. The toilet would likely need replacing, but once again you would try and maintain the look and feel. You could add a fresh coat of paint to give it a new feel, but you would probably pain in a period appropriate color.

As you can see, the differences in refurbishing versus remodeling come in cost, and end look and feel, but not necessarily in the way you get there. Repainting a cabinet can be done to refurbish it, or remodel it. So, the distinction can be difficult to make.