When looking at switches and buttons, you'll find a wide variety of terms to describe the switch action. Further, those terms will vary a little bit based on the type of switch as well. For example, it would be more common to see "latching" or "on/off" with a pushbutton switch, but not a rocker or toggle. Slide switches, which are typically not momentary, even have momentary versions, making it a vendor's decision whether or not to label the "normal" ones somehow.
Let's take a look at pushbutton switches at two popular vendors, Digikey and Mouser:
Any position on a switch that's momentary is denoted by the "Mom" abbreviation in the list. A pushbutton in the style you're looking for would then be found under the "Off-On" category. Here, "On" would mean it stays in that position, because otherwise they would use "Mom" to indicate that position is momentary.
Also note that "Off-Mom" and "On-Mom" would help distinguish what the switch does by default. The first being "off unless pushed" and the second being "on unless pushed."
Mouser uses parenthesis to indicate momentary positions. So "(ON)" here is the same as "Mom" above. They've also kind of went a bit overboard (IMO) and show the reciprocal function in some cases, so "OFF - ON, ON - OFF" just means you could have either position be off or on, depending on how you wire it. (This is the same as "OFF - ON" but my guess is manufacturer-provided data gets put into more than one category that should otherwise be combined.)
The number of poles (or common terminals) on a switch may also have something to do with unusual switch action filter options.
The switch you refer to is small, but I wouldn't call it surface mount. The tabs are certainly something you could surface mount if desired, but it appears to be a very small panel mount switch. Some panel mount switches have flanges or threads to mount through some sort of enclosure wall, others may have holes to allow mounting via screws, and still others (like the one you show) may just use a bit of glue or some sort of friction fit. An actual surface-mount/tactile switch (at least the ones I can find) is almost always momentary.
Adafruit provides the datasheet (or this) to their switch, but that probably doesn't help you source them. The closest I could find on Digikey is a Judco 40-4911-00. All that said, good quality switches can be expensive. If you're finding the Adafruit switch to be too expensive at USD $0.95 each, then you're not likely to find a better price unless you inquire about quantity discounts.