Question about installing SSD into a Macbook Pro

You can restore the backup onto the SSD so long as the SSD fits the entire contents of the backup^[1].

According to Apple's support pages, you do not need to use an Apple Time Capsule for backups:

Time Machine is the built-in backup feature of your Mac. To use it, you need an external storage solution, sold separately:

• External hard drive connected to a USB, FireWire, or Thunderbolt port on your Mac
• Time Capsule or macOS Server on your network
• External hard drive connected to the USB port of an AirPort Extreme Base Station on your network

Then you would want to restore using macOS recovery using the "Restore from Time Machine Backup" utility.

[1]: It's possible this is not the same as the size used by your hard drive, as the Time Machine backup also has previous versions of files and deleted files. However, since you are newly setting up Time Machine, there would be no previous versions of files.

...can I do a time machine backup of my current hard drive on an external hard drive, install the SSD, and then use the time machine backup from the external to transfer it onto the newly installed SSD?

Yes. This is a valid and accepted backup/restore technique. The advantage here is you don't need to worry about size differentials of the two drives (larger HDD than your SSD, for example).

Is this the same as using the clone program above?

No.

I would avoid this method when migrating from a HDD to an SSD.

Why?

Cloning is exactly what it's name implies - an exact copy of your drive down to the block level meaning blocks of data which were marked as deleted on the HDD but not overwritten get cloned to the SSD.

And herein lies the problem. Spinning drives delete files by deleting the pointer to the data (like deleting your address from government records but leaving the structure in tact). SSDs on the other hand goes in and marks the area as "unused" (not just deleting the address, but putting a note on the record that it's unused while sending a working to report back that the building doesn't exist).

When you clone, you will be cloning orphaned data that wasn't marked as unused but will subsequently write to that block.

(IMO) I would use this opportunity to do a clean install of macOS and migrate my data/settings over with Migration Assistant. It will take longer than a simple backup/restore, but you get the opportunity to start with a "clean slate" so to speak which will pay off in the future (you're not copying/restoring hidden issues you backed up)