What's the difference between the windows in my home now and replacement windows?

Regarding installation:
When your home was built, the window openings were made to accommodate a stock sized window, whereas replacement windows are typically manufactured to custom fit existing openings (see FAQ 2).

Regarding the window:
The most likely differences are reduced maintenance, ease of operation, and thermal performance features driven by new technologies.

How is replacing windows different than putting windows in when the house was built new?

Your house now has finished siding, walls, and trim which you probably want left intact after the windows are replaced to minimize disruption and cost. A replacement window is made to fit into your old window's sash opening (the area of glass including its frame and any hardware) and doesn't require the removal of interior or exterior casings. The installation of a new construction window (most likely what is being replaced) would require removal of the entire window including its jamb, head, sill, and casings to expose the stud opening. Although certainly an option, this method is more labor intensive and invasive and would involve walls and siding beyond the casings.

Windows are made with many different materials. What is the best material?
Wood? Vinyl? Aluminum?

As long as you are buying a window of quality, usage need be the only determinant of the best material. Vinyl offers great thermal properties in both welded and mechanical styles. Wood offers more color diversity and warmth where needed. Aluminum is used primarily in commercial applications. Fiberglass windows are available where structure and versatility are important. We can show you the differences and you can tell us what is best.