Is a 'seed phrase' independent of the type of wallet? I have had a few things happen on my PC and for the moment can't directly call up my bitcoin in its old wallet. There are files from various wallets sitting in my home directory but before I try to get a wallet program to retrieve from them, will find a piece of paper where I wrote a seed phrase. 

The question is, can this seed phrase be entered into any wallet, whether it is Armory, Electrum, Wasabi, Bither to get the bitcoin back, or must I be careful to install exactly the same wallet which gave me the seed phrase in the first place?
First of all, some software wallets imports are supporting only 12 word or 24 word combinations. 
Some support different BIPs and thus path derivation schemes (32/44/84) by default, and some only single one of them. 
Some have additional feature for a specific seed passphrase. 
All of the differences you can check on https://walletsrecovery.org/ 

So to answer your question, you have to install the wallet that uses the same seed format and path derivation as the one you've originally created.