If you need to get a storage space that you can have near your property, you have a choice between containers, which sit directly on the ground, and storage trailers, which are up on one to two rows of wheels. Sometimes choosing between them is easy; for example, if the items you're storing have to be with you every day no matter where you go, a trailer with wheels is what you need. But if that's not the case, then you need to look at other features to determine which style will work best for you.
Even if you're not towing the trailer daily for work, sometimes you need a more portable storage space. For example, if you're doing a lot of work on your home and need to move the trailer around periodically, a wheeled trailer is going to be necessary. A stationary container can still be moved, but it takes a lot more work and time -- not to mention money, as you may have to hire a separate hauler to come in and move the container.
One of the risks of having a wheeled, portable trailer is that it is easier to steal. With a container, thieves really have to break in and take time to get items rather than driving off with the entire thing. If you're very concerned about that, you have two options. One is to use a container with heavy locks and chains, and the other is to get a trailer that has added security measures like wheel locks and hitch locks.
Both trailers and containers can be large or small, but on the whole, you're average rental trailer for someone, say, doing some remodeling is going to be smaller than the container. You can get large containers that look like those on semi-trucks, while trailers are usually smaller to allow SUVs and pickups to tow them safely. That being said, you can still find some rather spacious trailers.
This one applies mainly to wheeled trailers. If you look at the ones available, you'll see mainly those with one row of wheels, or two rows adjacent to each other -- not two separate axles like you see on cars. If you're storing heavier items, try to get the two-row version.
Talk to trailer and container rental places about what exactly you need the trailer for. The more detail you can provide, the easier it will be for the company to point you toward the style that would work best for you.