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. With the looming FDA regulations on these types of products it's uncertain how long the current models on the market will be available.
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. Bud from VapeCritic.com keeps a running list of his top picks for best vape pen and best portable vaporizer, check them out to see which models are currently on top.
Portable vaporizers are those designed for use primarily with dry herbs, but many of them will work with concentrates as well. Good models will range in price from about $80 for an entry-level unit to $400 for the top of the line. One of the newest and coolest portable vapes on the market is the DaVinci IQ which is the pinnacle of conduction vaporizing. It goes directly head-to-head with the new PAX 3 since they're both conduction vapes priced at $275.
Generally, any vape that plugs in to 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. If performance and vapor production are your top concerns, this is type of vape you want.
Popular desktop models include the Volcano, VapeXhale Cloud EVO and Plenty. If you're not sure which one is right for you check out Vape Critic's reviews of the best vaporizers you can buy right now, there are a bunch of nice ones to choose from. Anyone who considers themselves a serious vaper has a good desktop vape, and if you partake often these save you a ton of money on material.