SD, SDHC and SDXC all physically look the same, therefore they’ll all fit in a regular SD card slot. The only thing you may need to check (especially for older devices) is the max capicity your device can take. Micro SD Cards are similiar, but smaller.
Many SD card manufacturers will also list a specific speed alongside the Class rating. This means a card can be Class 10 but also be listed as ‘up to 80MB/s’. The wording is important, as that’s the best you can expect but not necessarily what you’ll always achieve. On any type of SD card, the Class rating is denoted by a number inside of a C symbol. - FOR ALL TYPES OF SPEED CLASSES THE BIGGER NUMBER IS ALWAYS FASTER.
UHS came about due to 4K-capable video devices needing faster write speeds. The UHS Speed Class is denoted by either a 1 or 3 inside of a bucket U symbol. As a rule of thumb, 4K-capable camcorders will usually require at least a U3 rated SD card.
Note that unlike the UHS Speed Class, these are not sustained speeds.