Rectified Tiles

Rectified tiles are ceramic or porcelain tiles that have been precisely cut and machined to give them near-perfect straight edges and exact dimensions. These tiles provide a very clean, symmetrical look, and allow for extremely fine grout joints of 3mm or less (typically using LATICRETE PermaColor Grout or SpectraLock Pro Premium Epoxy Grout which, are most appropriate for grout joints as narrow as 1.5mm).  
Rectified tiles usually also have a very fine bevel around their top edge too, to help reduce the chance of their sharp edges chipping. For practical reasons, it's unusual to find rectified tiles smaller than about 300mm x 300mm.

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Non-Rectified Tiles

For a long time, non-rectified tiles were the industry standard, making them incredibly common in homes that are not newly-built or haven’t been renovated in a while. Basically, a non-rectified tile is any tile that has been pressed and the edges have not been precisely cut and machined to give them near-perfect straight edges and exact dimensions which, results in each tile having a plain generally rolled edge.
Because of this imprecise process, each tile is not the exact same size. From an installation perspective, which means larger grout lines will need to be used in order to correctly fit these tiles together, fill in the gaps, and hide their little differences (typically using LATICRETE Permacolor Grout or SpectraLock Pro Premium Epoxy Grout) which, are most appropriate for wider grout lines up to 12mm).  
This works fine, but the resulting large grout lines are not as aesthetically pleasing to most people, and also require more cleaning and maintenance (using LATICRETE StoneTech® Cleaners and Sealers is recommended).

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Exterior Tiles

Also referred to as external tiles, grip tiles and outdoor tiles. These come in a variety of shapes and sizes, textures and finishes. Some with a rough sandpaper type finish and others with more of a pressed undulating type finish. All outdoor tiles have a matt or natural finish. When selecting an exterior grip finish tile, one must consider porcelain tile only. Porcelain tile is frost resistant, whereas ceramic tile is not. The NZ Standard for rating a grip tile suggests that when wet a grip tile must meet the CO Efficient of Friction using the Pendulum Test Method with a pass being 0.40 or greater. In this modern era most outdoor tile will have a matching indoor tile to create seamless indoor outdoor flow. Exterior tiles are harder to clean due to their rough textured nature but with the correct chemicals and a stiff bristle broom they are easy to maintain using LATICRETE StoneTech® Cleaners.

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Interior Tiles

Also referred to as internal tiles and indoor tiles. These come in a variety of shapes and sizes and finishes. They can be natural or matt finish, semi polished, Lappato or Patinato finish or polished. Sizes vary from 7.5cmx10cm or can be as large as 1.6m x 3.2m and can be installed on floors and walls. Most indoor tile nowadays is produced using a porcelain clay body with a glazed surface. However some manufacturers still chose to produce with a red or white clay biscuit. The porcelain body allows for greater technical design utilizing High Definition 3D Inkjet Printing Technology. These designs allow the user to achieve the look of Natural Stone without the problems that natural stone can cause. Porcelain is much harder than ceramic tile.

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Tile Surface Finishes

Natural – Generally a Matt finish
Matt - Generally a Natural finish 
Semi-Gloss - As the name suggests is a Semi Polished finish
Semi Polished – As the name suggests is a Semi-Gloss finish
Polished – As the name suggests provides a very reflective finish similar to glass or mirror 
Lappato or Patinato – Is Italian for semi polished 
Grip – As the name suggests is a rough and textured finish that would normally be used for outdoor, wet areas and where a non-slip surface is required