Taxi Stand means only Taxi can wait and stop there.
Taxi Stop means only Taxi can either pick up or drop off but they cannot wait.
Pick Up/Drop Off Point means all vehicles can either pick up or drop off but they cannot wait.
This is why private hirers can NEVER pick up/drop off passengers at a taxi stand.
It is illegal for private hirers to pick up/drop off passengers at a taxi stand because they will be penalised and/or fine.
Here are the taxi stand/taxi stop/pick up/drop off within CBD:
I just found a website called TaxiRouter SG. The website is really useful.
You can explore all the available taxis and taxi stands in Singapore.
Basically, you will be able to know whether there is available taxis in your area.
The site was built by Lim Chee Aun. Thank you for making the website useful for others.