I have the same apps on my Mac that I have always had, yet all of a sudden I am getting a message saying I am out of memory and must

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Use the Activity Monitor application and make sure to use View >> View All Processes

What process or processes are using the Most CPU and Memory.

Often times - the issue maybe not be a single Process but a combination of Processes

Also, when the computer is using some much Memory - it can be a indicator of a Lack Of Empty Spaces on the Drive.

In which case, the CPU and Memory usage would become Much More because it is searching for Empty Space to safe all the Changes the user is performing.

Images below from Activity Monitor 1 - CPU usage and 2 - Memory Usages

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It is generally a good computer practice to alway keep at least 15% to 20% of the Total Drive Capacity’s as Empty Space. Allowing the computer to drop below these guidelines may eventually, cause unintended consequences.

There is Purgeable Space and there is Empty Space.

Purgeable Space which is Controlled by the Operating System. When the Operating Systems decides the computer needs additional Empty Space, it will move a portion of the Purgeable to Empty space

AFAIK - there is no User Actions to hasten this transition from Purgeable to Empty Space

It can day or longer before this will occur  

The links below will assist in identifying what is taking up space on the Internal Drive and provide possible ways to remove data that is under the direct control of the User ( Home Folder ) . 

Rebuild the Spotlight index on your Mac

What is “Other” storage on a Mac, and how can I clean it out?

Free up storage space on your Mac

OmniDiskSweeper Safe to use

GrandPerspective 

How to delete Time Machine snapshots on your Mac.  

Often caused if the Time Machine Drive has not been attached  to the computer and TM Backup is set to run on a Schedule. 

TM Backup will make Snap Shot on the Internal Drive awaiting the TM Backup Drive to be attached. 

Only then will the Snaps Shots be transferred to the External Drive and deleted the Internal Drive.

See used and available storage space on your Mac

Locate backups of your iPhone, iPad, and iPod touch

Notation - If the user is using a cloning software like Carbon Copy Cloner - suggest tweaking the Safety Net Feature in this software. It may be making additional Snap Shots that are not being Cloned to the Eternal Drive. If this should be the case, these Snap Shot could be using additional space on the drive 

There are 2 reasons for the "Your system has run out of application memory" dialog box.

A) Your boot disk has very low free storage, and macOS cannot create page/swap files to offload virtual memory contents to disk. This is generally not the case, but I mention this because if you do have very low free storage, it might apply. Depending on how much virtual memory is being called for, anything under 50-100GB of free storage may trigger the message.

Apple menu (upper left corner) -> About This Mac -> Storage (tab)

B) A process (or set of processes) has asked macOS for excessive amounts of virtual memory address space. Virtual memory address space requires macOS to create Virtual Memory Page Tables in non-pageable kernel address space to keep track of the application virtual addresses given out. Generally, if there is a memory leak (process asks for a virtual address range, uses the addresses, forgets to give them back, asks for another virtual address range, uses the addresses, forgets again, wash, rinse, repeat), eventually there are so many non-pageable virtual memory page table entries trying to keep track of the virtual addresses, that macOS no longer has memory available for applications, and you get the "Your system has run out of application memory"

If you look at

Applications -> Utilities -> Activity Monitor -> View (menu) -> All Processes -> Memory (tab)

you can see what processes are using lots of memory. Many of these processes will NOT be applications. Just background agents and daemons used to provide many of the macOS services, as well as 3rd party background processes doing whatever that 3rd party app thinks it should be doing.

Also keep in mind that each web browser tab will be a separate process running its own Javascript. If you have lots of browser tabs open, or if one of the browser tabs running Javascript with a bug in it, it is possible these browser tabs will add up to a lot of virtual memory demands, but no individual tab will look all that big.

If you have a limited amount of RAM it may be helpful to (1) restart your computer in the Safe Mode and (2) clear the browser's history. And, as noted, don't keep a lot of apps and windows open if you aren't using them. To restart in the Safe Mode, hold down the Shift key on restart. This can take several minutes while the OS is repairing itself and emptying its caches. Then restart normally. Some Macs will allow user installed additional RAM. You might also look into that possibility.

What is the total capacity of your startup drive?

How much of that capacity is available?

To find out, right-click (or Control-click) the drive icon in the desktop and select Get Info.