All phone chargers (and AC adapters in general) have a current limit by design. Current is usually measured in Amps (which is the short form for Amperes). The current rating should be listed in the small print in your phone charger. The image below shows a charger with a 5V DC output (USB standard voltage) with a max current of 1.2A or 1200mA.
So to answer your question, some chargers can output 500mA, others 1A, or more. More current means your phone will charge faster. More current also means your battery will get hotter. This is usually not a problem since modern phones have an internal current limiter to prevent overheating (unless you get the Galaxy Note 7). But back in the day, phones didn’t have a limiter and plugging in a higher current charger could have fried your phone. Older chargers were limited to 500mA (or 0.5A) since that was the standard for USB 1.0 and USB 2.0
The more output current of the charger the quicker charging will be. Buy at least 2A chargers. Pay attention to quick charging technologies.
The main parameters affecting a phone charging speed with a specific charger is the current produced by charger. The more is the current the quicker is the charging speed. However, each phone sets maximum of current it may consume.
Recently most phones consume current of up to 2A. If you connect them to a charger producing less than 2A, the charging will be significantly slower. Thus, don’t buy a charger which produces less than 2A. However, there will be no speed increase if you replace 2A charger by 9A charger for a phone which knows to consume only 2A.
Every charger normally has a label specifying OUTPUT current (in mA or A – milliamperes or amperes). The charger on the picture produces 550mA (0.55A) – which was good for old phones and not enough for the newer ones.
It’s much more difficult to find current consumed by a phone. The easiest way is to find the phone’s original charger label – it will normally fit the current of the phone. If you don’t know – use a charger producing current of at least 2A.
The matter became event more complex after many companies started to use different quick-charge technologies. Look for the phone specification in the web. The names to look are QuickCharge 2.0 or 3.0, Dash (OnePlus phones), TurboPower (Motorola phones), USB-C charger, Lightning (iPhones) etc.
To get the best charging times for the phones with all these technologies you should get a charger which supports the same technology.
The last but not least, there are some chargers which are low quality and fail to give the current according their labeling, thus slowing the charging time. Fortunately, this is not frequent scenario.