Vape mods are the powerplant, they contain the battery and attach to tanks and atomizers that hold your e-liquid. These are also sometimes called "vape pens" depending on the size and style, but this category refers to vapes that replace e-cigs and work with e-juice.
Sometimes beginners start out with a vape that looks like a cigarette (e-cig), then eventually upgrade to a pen-style unit with a tank or clearomizer to hold the e-liquid. Intermediate and advanced users tend to gravitate towards Mods because the possibilities for customization are endless.
Vaporizer pens are generally known to be those that work with wax and oil concentrates. Some of these closely resemble the look and feel of an e-cig or e-liquid pen, but the atomizer or coil where you place your material is a bit different.
Portable vaporizers are those designed for use primarily with dry herbs, but many of them will work with concentrates as well. Examples of very popular portable vapes include the PAX, Crafty and Firefly. Check out this YouTube video by The Vape Critic to quickly figure out the best portable vaporizer for you.
Generally, any vape that plugs into an outlet for power is considered a desktop vaporizer. These are made for use with dry herbs and concentrates, and the expensive ones tend to be pretty robust in size and performance.
Popular desktop models include the Volcano, VapeXhale Cloud and Sublimator. If you're not sure which one is right for you, check out Vape Critic's reviews of the best vaporizers you can buy. Anyone and everyone who considers themselves a serious vaper has a good desktop vape, and if you partake often these save a ton of material.